1. The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.4 days and a standard deviation of 2.1 days. What is the median recovery time? _____ days

2. The patient recovery time from a particular surgical procedure is normally distributed with a mean of 6.9 days and a standard deviation of 1.3 days. What is the z-score for a patient who takes 8 days to recover? (Round your answer to two decimal places.) z = _____

3. Kyle's doctor told him that the z-score for his systolic blood pressure is 1.75. Which of the following is the best interpretation of this standardized score? The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean = 125

and standard deviation = 11. If X = a systolic blood pressure score then X ~ N(125, 11).

(a) Which answer(s) is/are correct? (Select all that apply.) 1. Kyle's systolic blood pressure is 1.75 standard deviations above the average systolic blood pressure for men.

2. Kyle's systolic blood pressure is 175.

3. Kyle's systolic blood pressure is 1.75 times the average blood pressure of men his age.

4. Kyle's systolic blood pressure is 1.75 above the average systolic blood pressure of men his age. (b) Calculate Kyle's blood pressure. (Enter an exact number as an integer, fraction, or decimal.)

4. The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.6 days and a standard deviation of 1.8 days. What is the probability of spending more than 2 days in recovery? (Round your answer to four decimal places.)

5. The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.5 days and a standard deviation of 2.2 days. What is the 75th percentile for recovery times? (Round your answer to two decimal places.) ____ days

6. The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 6 minutes and a standard deviation of 2 minutes. Find the probability that it takes at least 9 minutes to find a parking space. (Round your answer to four decimal places.)

7. The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 5 minutes and a standard deviation of 3 minutes. Eighty percent of the time, it takes more than how many minutes to find a parking space? (Round your answer to two decimal places.) ___ min

8. IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual.

(A) Give the distribution ofX. X~ ____ ( ____ , ____ )

(B) Find the probability that the person has an IQ greater than110. Write the probability statement. P( _____ ) What is the probability? (Round your answer to four decimal places.)

________

(C) Mensa is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the Mensa organization. Write the probability statement.

P(X > x) = ______

What is the minimum IQ? (Round your answer to the nearest whole number.) x = _____

(D) The middle 80% of IQs fall between what two values? Write the probability statement.

P(x₁ < X < x₂) = _____

State the two values. (Round your answers to the nearest whole number.)

x₁ =

x₂ =

9. Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 210 feet and a standard deviation of 40 feet. Let X = distance in feet for a fly ball.

(A) Give the distribution ofX. X~ ____ ( ____ , ____ )

(B) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 182 feet? (Round your answer to four decimal places.)

(C) Find the 80th percentile of the distribution of fly balls. (Round your answer to one decimal place.) ____ ft

(D) Write the probability statement. (Let k represent the score that corresponds to the 80th percentile.)

P(X < k) = _____

10. In China, four-year-olds average three hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.5 hours and the amount of time spent alone is normally distributed. We randomly survey one Chinese four-year-old living in a rural area. We are interested in the amount of time the child spends alone per day.

(A) In words, define the random variable X.

1. the time (in hours) a four-year-old in China spends unsupervised per week

2. the time (in hours) a four-year-old in China spends unsupervised per day

3. the time (in hours) a child in China spends unsupervised per day

4. the number of Chinese people that live in rural areas

5. the number of four-year-old Chinese children that live in rural areas

(B) X~ ____ ( ____ , ____ )

(C) Find the probability that the child spends less than 1 hour per day unsupervised. Write the probability statement.

P(________)

What is the probability? (Round your answer to four decimal places.)

(D) What percent of the children spend over 10 hours per day unsupervised? (Round your answer to four decimal places.)

(E) 80% of the children spend at least how long per day unsupervised? (Round your answer to two decimal places.)

_____ hr

11. Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 24 days and a standard deviation of 8 days.

(A) In words, define the random variable X.

1. the length, in hours, of a criminal trial

2. the number of trials that last 24 days

3. the mean time of all trials

4. the length, in days, of a criminal trial

(B) X~ ____ ( ____ , ____ )

(C) If one of the trials is randomly chosen, find the probability that it lasted more than 28 days. (Round your answer to four decimal places.)

Write the probability statement.

P (_______)

(D) 80% of all trials of this type are completed within how many days? (Round your answer to two decimal places.)

______ days

12. Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a seven-lap race) with a standard deviation of 2.28 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps.

(A) In words, define the random variable X.

1. the distance (in miles) of each race

2. the distance (in miles) of each lap

3. the time (in seconds) per race

4. the time (in seconds) per lap

(B) X~ ____ ( ____ , ____ )

(C) Find the percent of her laps that are completed in less than 134 seconds. (Round your answer to two decimal places.)

(D) The fastest 4% of her laps are under how many seconds? (Round your answer to two decimal places.)

(E) Enter your answers to two decimal places. The middle 70% of her lap times are from ______ seconds to ______ seconds.