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mathematics
statistics

Questions and Answers of Statistics

The Wechsler Intelligence Scale for Children is approximately normally distributed, with mean 100 and standard deviation 15. (a) What is the probability that a randomly selected test taker will score
According to major league baseball rules, the ball must weigh between 5 and 5.25 ounces. A factory produces baseballs whose weights are approximately normally distributed, with mean 5.11 ounces and
According to a Gallup poll, 46% of Americans 18 years old or older stated that they had read at least six books (ﬁction and nonﬁction) within the past year. You conduct a random sample of 250
In 1798, Henry Cavendish obtained 27 measurements of the density of Earth, using a torsion balance. The following data represent his estimates, given as a multiple of the density of water. Is it
According to a USA Today “Snapshot,” 20% of adults surveyed do their most creative thinking while driving. You conduct a survey of 250 adults and ﬁnd that 30 do their most creative thinking
A continuous random variable X is uniformly distributed with 0 ≤ X ≤ 20. (a) Draw a graph of the uniform density function. (b) What is P(0 ≤ X ≤ 5)? (c) What is P(10 ≤ X ≤ 18)?
List the properties of the normal density curve.
Use the ï¬gure to answer the questions that follow:(a) What is µ? (b) What is Ïƒ? (c) Suppose that the area under the normal curve to the left of x = 10 is 0.9332.
Draw a standard normal curve and shade the area to the right of z = 2.04. Then ﬁnd the area of the shaded region.
Find the z-scores that separate the middle 88% of the data from the area in the tails of the standard normal distribution.
Find the value of z0.04.
(a) Draw a normal curve with µ = 20 and σ = 3. (b) Shade the region that represents P(22 ≤ X ≤ 27) and ﬁnd the probability.
Suppose that the talk time on the Apple iPhone is approximately normally distributed with mean 7 hours and standard deviation 0.8 hour. (a) What proportion of the time will a fully charged iPhone
The waist circumference of males 20 to 29 years old is approximately normally distributed, with mean 92.5 cm and standard deviation 13.7 cm. (a) Use the normal model to determine the proportion of
Suppose the scores earned on Professor McArthur’s third statistics exam are normally distributed with mean 64 and standard deviation 8. Professor McArthur wants to curve the exam scores as follows:
In a poll conducted by the Gallup organization, 16% of adult, employed Americans were dissatisﬁed with the amount of their vacation time. You conduct a survey of 500 adult, employed Americans.(a)
A continuous random variable X is uniformly distributed with 10 ≤ X ≤ 50. (a) Draw a graph of the uniform density function. (b) What is P(20 ≤ X ≤ 30)? (c) What is P(X < 15)?
Imagine that a friend of yours is always late. Let the random variable X represent the time from when you are supposed to meet your friend until he shows up. Suppose your friend could be on time (x =
Imagine that a friend of yours is always late. Let the random variable X represent the time from when you are supposed to meet your friend until he shows up. Suppose your friend could be on time (x =
Imagine that a friend of yours is always late. Let the random variable X represent the time from when you are supposed to meet your friend until he shows up. Suppose your friend could be on time (x =
Imagine that a friend of yours is always late. Let the random variable X represent the time from when you are supposed to meet your friend until he shows up. Suppose your friend could be on time (x =
The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution. (a) Draw the graph of
The reaction time X (in minutes) of a certain chemical process follows a uniform probability distribution with 5 ≤ X ≤ 10. (a) Draw the graph of the density curve. (b) What is the probability
One graph in the ï¬gure represents a normal distribution with mean µ = 10 and standard deviation Ïƒ = 3. The other graph represents a normal distribution with mean
One graph in the ï¬gure at the top of the next column represents a normal distribution with mean µ = 8 and standard deviation Ïƒ = 2. The other graph represents a
Draw a normal curve with µ = 30 and σ = 10. Label the mean and the inﬂection points.
Draw a normal curve with µ = 50 and σ = 5. Label the mean and the inﬂection points.
Monthly charges for cell phone plans in the United States are normally distributed with mean µ = +62 and standard deviation σ = +18. (a) Draw a normal curve with the parameters labeled. (b) Shade
The lives of refrigerators are normally distributed with mean µ = 14 years and standard deviation σ = 2.5 years. (a) Draw a normal curve with the parameters labeled. (b) Shade the region that
The birth weights of full-term babies are normally distributed with mean µ = 3400 grams and σ = 505 grams. (a) Draw a normal curve with the parameters labeled. (b) Shade the region that represents
The heights of 10-year-old males are normally distributed with mean µ = 55.9 inches and σ = 5.7 inches. (a) Draw a normal curve with the parameters labeled. (b) Shade the region that represents the
The lengths of human pregnancies are normally distributed with µ = 266 days and Ïƒ = 16 days.(a) The ï¬gure represents the normal curve with µ = 266 days and
Elena conducts an experiment in which she ï¬lls up the gas tank on her Toyota Camry 40 times and records the miles per gallon for each ï¬ll-up. A histogram of the miles
In the game of golf, distance control is just as important as how far a player hits the ball. Michael went to the driving range with his range ï¬nder and hit 75 golf balls with his
The following frequency distribution represents the heights (in inches) of 80 randomly selected 5-year-old females.(a) Use MINITAB or some other statistical software to construct a relative frequency
Determine the area under the standard normal curve that lies to the left of (a) z = -2.45 (b) z = -0.43 (c) z = 1.35 (d) z = 3.49 Find the indicated areas. Be sure to draw a standard normal curve
Determine the area under the standard normal curve that lies to the left of (a) z = -3.49 (b) z = -1.99 (c) z = 0.92 (d) z = 2.90 Find the indicated areas. Be sure to draw a standard normal
Determine the area under the standard normal curve that lies to the right of (a) z = -3.01 (b) z = -1.59 (c) z = 1.78 (d) z = 3.11 Find the indicated areas. Be sure to draw a standard normal
Determine the area under the standard normal curve that lies to the right of (a) z = -3.49 (b) z = -0.55 (c) z = 2.23 (d) z = 3.45 Find the indicated areas. Be sure to draw a standard normal
Determine the area under the standard normal curve that lies between (a) z = -2.04 and z = 2.04 (b) z = -0.55 and z = 0 (c) z = -1.04 and z = 2.76 Find the indicated areas. Be sure to draw a standard
Determine the area under the standard normal curve that lies between (a) z = -2.55 and z = 2.55 (b) z = -1.67 and z = 0 (c) z = -3.03 and z = 1.98 Find the indicated areas. Be sure to draw a standard
Determine the total area under the standard normal curve (a) to the left of z = -2 or to the right of z = 2 (b) to the left of z = -1.56 or to the right of z = 2.56 (c) to the left of z = -0.24 or to
Determine the total area under the standard normal curve (a) to the left of z = -2.94 or to the right of z = 2.94 (b) to the left of z = -1.68 or to the right of z = 3.05 (c) to the left of z = -0.88
Find the value of za . z0.01
Find the value of za . z0.02
Find the value of za . z0.025
z0.15 Find the value of za .
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Find each indicated percentile for X. The 9th percentile?
The 90th percentile Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Find each indicated percentile for X.
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Find each indicated percentile for X. The 81st percentile?
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Find each indicated percentile for X. The 38th percentile?
The mean incubation time of fertilized chicken eggs kept at 100.5°F in a still-air incubator is 21 days. Suppose that the incubation times are approximately normally distributed with a standard
The reading speed of sixth-grade students is approximately normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute.(a) What is the probability that a
The number of chocolate chips in an 18-ounce bag of Chips Ahoy! chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and standard deviation 118 chips according to a
Fast-food restaurants spend quite a bit of time studying the amount of time cars spend in their drive-throughs. Certainly, the faster the cars get through the drive-through, the more the opportunity
The lengths of human pregnancies are approximately normally distributed, with mean µ = 266 days and standard deviation σ = 16 days. (a) What proportion of pregnancies lasts more than 270 days? (b)
Electric manufactures a decorative Crystal Clear 60-watt light bulb that it advertises will last 1500 hours. Suppose that the lifetimes of the light bulbs are approximately normally distributed, with
Steel rods are manufactured with a mean length of 25 centimeters (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed, with a
Ball bearings are manufactured with a mean diameter of 5 millimeters (mm). Because of variability in the manufacturing process, the diameters of the ball bearings are approximately normally
In sports betting, Las Vegas sports books establish winning margins for a team that is favored to win a game. An individual can place a wager on the game and will win if the team bet upon wins after
In games where a team is favored by more than 12 points, the margin of victory for the favored team relative to the spread is normally distributed with a mean of -1.0 point and a standard deviation
The mean incubation time of fertilized chicken eggs kept at 100.5°F in a still-air incubator is 21 days. Suppose that the incubation times are approximately normally distributed with a standard
The reading speed of sixth-grade students is approximately normal, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute. (a) What is the reading speed of a
The number of chocolate chips in an 18-ounce bag of Chips Ahoy! chocolate chip cookies is approximately normally distributed, with a mean of 1262 chips and a standard deviation of 118 chips,
Fast-food restaurants spend quite a bit of time studying the amount of time cars spend in their drive-through. Certainly, the faster the cars get through the drive-through, the more the opportunity
The time required for Speedy Lube to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 17 minutes and a standard deviation of 2.5
The following data represent the distribution of birth weights (in grams) for babies in which the pregnancy went full term (37 to 41 weeks).Birth Weight (g) ....Number of Live Births0–499
The ACT and SAT are two college entrance exams. The composite score on the ACT is approximately normally distributed with mean 21.1 and standard deviation 5.1. The composite score on the SAT is
In a 1998 advertising campaign, Nabisco claimed that every 18-ounce bag of Chips Ahoy! Cookies contained at least 1000 chocolate chips. Brad Warner and Jim Rutledge tried to verify the claim. The
A random sample of college students aged 18 to 24 years was obtained, and the number of hours of television watched in a typical week was recorded.(a) Use the following normal probability plot to
A random sample of O-rings was obtained, and the wall thickness (in inches) of each was recorded.Use a normal probability plot to assess whether the sample data could have come from a population that
A random sample of weekly work logs at an automobile repair station was obtained, and the average number of customers per day was recorded.Use a normal probability plot to assess whether the sample
A random sample of 20 undergraduate students receiving student loans was obtained, and the amount of their loans for the 2011€“2012 school year was recorded.Use a normal probability plot to
A random sample of 25 years between 1890 and 2011 was obtained, and the amount of snowfall, in inches, for Memphis was recorded.Use a normal probability plot to assess whether the sample data could
Suppose X is a binomial random variable. To approximate P(X < 5), compute_______.
Suppose X is a binomial random variable. To approximate P(3 ≤ X ≤ 10), compute ____________.
The probability that at least 40 households have a gas stove A discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution.
The probability of no more than 20 people who want to see Roe v. Wade overturned A discrete random variable is given. Assume the probability of the random variable will be approximated using the
The probability that exactly eight defective parts are in the shipment A discrete random variable is given. Assume the probability of the random variable will be approximated using the normal
The probability that exactly 12 students pass the course A discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution.
The probability that the number of people with blood type O-negative is between 18 and 24, inclusive A discrete random variable is given. Assume the probability of the random variable will be
The probability that the number of tornadoes that occur in the month of May is between 30 and 40, inclusive A discrete random variable is given. Assume the probability of the random variable will be
The probability that more than 20 people want to see the marriage tax penalty abolished A discrete random variable is given. Assume the probability of the random variable will be approximated using
The probability that fewer than 40 households have a pet A discrete random variable is given. Assume the probability of the random variable will be approximated using the normal distribution.
The probability that more than 500 adult Americans support a bill proposing to extend daylight savings time A discrete random variable is given. Assume the probability of the random variable will be
The probability that fewer than 35 people support theprivatization of Social Security A discrete random variable is given. Assume the probability of the random variable will be approximated using the
n = 60, p = 0.4, x = 20Compute P(x) using the binomial probability formula. Then determine whether the normal distribution can be used as an approximation for the binomial distribution. If so,
n = 80, p = 0.15, x = 18Compute P(x) using the binomial probability formula. Then determine whether the normal distribution can be used as an approximation for the binomial distribution. If so,
n = 40, p = 0.25, x = 30 Compute P(x) using the binomial probability formula. Then determine whether the normal distribution can be used as an approximation for the binomial distribution. If so,
n = 100, p = 0.05, x = 50 Compute P(x) using the binomial probability formula. Then determine whether the normal distribution can be used as an approximation for the binomial distribution. If so,

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