1. The heights of adult men in America are normally distributed, with a mean of 69.4 inches and a standard deviation of 2.62 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.5 inches and a standard deviation of 2.51 inches. a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)? z =

b) What percentage of men are SHORTER than 6 feet 3 inches? Round to nearest tenth of a percent. ____ %

c) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)? z =

d) What percentage of women are TALLER than 5 feet 11 inches? Round to nearest tenth of a percent. ____%

e) Who is relatively taller: a 6'3" American man or a 5'11" American woman? Defend your choice in a meaningful sentence.

2. The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 122 and standard deviation of 19 . Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher. a. Around what percentage of adults in the USA have stage 2 high blood pressure? Give your answer rounded to two decimal places. ___%

b. If you sampled 2000 people, how many would you expect to have blood pressure greater than 160? Give your answer to the nearest person. ____ people c. Stage 1 high BP is specified as systolic BP between 140 and 160. What percentage of adults in the US qualify for stage 1?

____ % d. Your doctor tells you you are in the 30th percentile for blood pressure among US adults. What is your systolic BP? Round to 2 decimal places. ____ lbs

3. For the past few month, a couple have been visiting preschools in Camarillo, CA for their 3-year-old daughter. The annual cost of preschool in Camarillo is assumed to be normally distributed with a mean of $8,407, and standard deviation of $2,662. Let X be the annual tuition of a random selected preschool in Camarillo.

1. If a Camarillo preschool is randomly chosen, find the probability that its annual tuition is below $5,745.
2. If a Camarillo preschool is randomly chosen, find the probability that its annual tuition is between $5,745 and $7,076.
3. The mid-70% of the Camarillo preschool cost is between ____ and _____ .

4. The mean daily production of a herd of cows is assumed to be normally distributed with a mean of 37 liters, and standard deviation of 6.7 liters. Let X be the production of a randomly selected cow in liters.

1. If a cow is randomly chosen, find the probability that its production is less than 20.2 liters.
2. If a cow is randomly chosen, find the probability that its production is between 47.1 and 57.2 liters.
3. The 87th percentile of the milk production is how many liters?

5. The lengths of pregnancies in a small rural village are normally distributed with a mean of 266 days and a standard deviation of 14 days. Let X be the length of a randomly recorded pregnancy in the village.

1. If a pregnancy randomly chosen in the village, find the probability that it lasted beyond 245 days.
2. If a pregnancy randomly chosen in the village, find the probability that it lasted between 273 and 294 days.
3. The 65th percentile pregnancy length in this village is days.

6. Using all 1991 birth records in the computerized national birth certificate registry compiled by the National Center for Health Statistics (NCHS), statisticians Traci Clemons and Marcello Pagano found that the birth weights of babies in the United States are not symmetric ("Are babies normal?" The American Statistician, Nov 1999, 53:4). However, they also found that when infants born outside of the "typical" 37-43 weeks and infants born to mothers with a history of diabetes are excluded, the birth weights of the remaining infants do follow a Normal model with mean ? = 3473 g and standard deviation ? = 475 g. Let X be the weight of a randomly selected infant born from 37 to 43 weeks whose mother did not have a history of diabetes.

1. If a healthy infant is randomly chosen, find the probability that the birth weight is beyond 3235 g.
2. If a healthy infant is randomly chosen, find the probability that the birth weight is between 2760 g and 3473 g.
3. The mid-90% of the healthy infant weight is between ____ g and_____ g.

7. The mean amount of time it takes a kidney stone to pass is 13 days and the standard deviation is 4 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible. a. Find the probability that a randomly selected person with a kidney stone will take longer than 15 days to pass it. b. Find the minimum number for the upper quarter of the time to pass a kidney stone. days.

8. Private nonprofit four-year colleges charge, on average, $26,109 per year in tuition and fees. The standard deviation is $6,576. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible. a. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 25,716 per year. b. Find the 66th percentile for this distribution. $ (Round to the nearest dollar.)

9. The average American man consumes 9.7 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.9 grams. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible. a. Find the probability that this American man consumes between 10.3 and 12.3 grams of sodium per day. b. The middle 30% of American men consume between what two weights of sodium? Low: High:

10. Complete the following statements.

in general, ____% of the values in a data set lie at or below the 98th percentile. ____% of the values in a data set lie at or above the 68th percentile.

if a sample consists of 500 test scores, ____ of them would be at or below the 46th percentile.

if a sample consists of 500 test scores, ___ of them would be at or above the 40th percentile.

11. The study by P. Motiani et al. compares two different agents, intrathecal sufentanil and fentanyl, used in enhancing the anesthesiology of patients receiving major lower limb surgery. One variable compared between the two agents was the amount of blood loss during the surgery. Based on the study, we will assume that amount of blood loss during major lower limb surgery using fentanyl is normally distributed with a mean 258.5 ml and a standard deviation of 59.2 ml. Let X be the amount of blood loss during major lower limb surgery using fentanyl of a randomly selected patient.

a. Find the probability that the amount of blood loss during major lower limb surgery using fentanyl of a randomly selected patient is

1. less than 304.8 ml. (Round the answer to 4 decimal places)
2. between 371.7 and 412.1 ml. (Round the answer to 4 decimal places)
3. more than 433.7 ml. (Round the answer to 4 decimal places)

b. Find the 30-th percentile for the amount of blood loss during major lower limb surgery using fentanyl. ml (Round the answer to 1 decimal place)

12. Assume that IQ scores are normally distributed with a mean 101 pts and a standard deviation of 11.7 pts. Let X be the IQ score of a randomly selected person.

a. Find the probability that the IQ score of a randomly selected patient is

1. less than 128.3 pts. (Round the answer to 4 decimal places)
2. between 77 and 116.9 pts. (Round the answer to 4 decimal places)
3. more than 131.5 pts. (Round the answer to 4 decimal places)

b. Find the 65-th percentile for the IQ score. pts (Round the answer to 1 decimal place)

13.

Areas Under the Curve: Percentiles Applications A percentile is the data value where a given percent falls below the data value. The graphs below show the graphs for various percentiles. Use the z-scores and the mean and standard deviation of the distribution to find the percentile. The area shaded in the graph represents the percent of all data values below z = 1.64. The shaded area equals 95%. -3 -2 -1 1 2 -score Q An exam score is normally distributed with a mean of 73 points and a standard deviation of 7 points. Find the exam grade for the 95th percentile. 95th percentile is points The area shaded in the graph represents the percent of all data values below z = 1.28. The shaded area equals 90%. -3 -2 -1 1 : 2 z-score The weight for an adult male german shorthaired pointer is normally distributed with a mean of 62 pounds and a standard deviation of 2 pounds. Find the weight in pounds for the 90th percentile. 90th percentile is poundsThe area shaded in the graph represents the percent bf all data values below 3 = 2.33. The shaded area equals 9996. zsca re The number cf skittles in a 7 b: bag is nbrmalli.r distributed a with mean of 194 pieces and a standard deviation of '5 pieces. Find the number of skittles for the 99th percentile. 99 th percentile is l:l