Work sheet #4 STA 2023
1) The test scores in a Statistics class have a mean of 75 and a standard deviation of 12. Use the Empirical Rule to give the range of scores that includes a) about 68% of the scores on this test, b) about 95% of the scores on this test, c) would a score of 50 be unusual or not unusual?
2) The heights of women have a mean of 63.6 inches and a standard deviation of 2.5 inches. Use the Empirical Rule to find the range of heights that include a) about 68% of the women, b) about 95% of women, c) would a height of 5 ft. 10 in. be unusual or not unusual?
3) IQ scores have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. Use the Empirical rule to tell a) what percentage falls between 70 and 130, b) what percentage falls between 85 and 115.
4) Batteries of 2 brands are compared. Brand A has a mean life of 48 months and a standard deviation of 2 months. Brand B has a mean of 48 months and a standard deviation of 6 months. Which brand would you say is the better choice? Why?
5) IQ scores have a mean of 100 and a standard deviation of 15. Kelly took the test and scored 130.
a) What is the difference between Kelly’s score and the mean?
b) How many standard deviations is that?
c) Convert Kelly’s score to a z-score.
d) How do your answers to b and c compare?
6) Women’s heights have a mean of 63.6 inches and a standard deviation of 2.5 inches. Jodi is 61.1 inches tall.
a) What is the difference between Jodi’s height and the mean?
b) How many standard deviations is that?
c) Convert Jodi’s height to a z-score.
d) How do your answers to b and c compare?
7) Heights of men have a mean of 69.0 inches and a standard deviation of 2.8 inches.
Find each of the following z-scores and tell if it is unusual.
a) Shaquille O’Neal is 7 ft. 1 in. tall.
b) Bob Jenkins 5 ft. 4 in.
c) Textbook’s author 69.72 inches tall.
8) Human body temperatures have a mean of 98.2o and a standard deviation of 0.62o. Find each z-score and tell if it is unusual.
a) 100o b) 96.96o c) 98.2o d) 101.3o
9) Scores on a History test have a mean of 80 and a standard deviation of 12. Scores on a Psychology test have a mean of 30 and a standard deviation of 8. Which is better: a score of 75 on the History test or a score of 27 on the Psychology test?
10) Test 1 has a mean of 128 and s = 34. Test 2 has a mean of 86 and s = 18. Test 3 has a mean of 15 and s = 5. Which of these scores is the highest relative score? Test 1 score of 144 or Test 2 score of 90 or Test 3 score of 18
11) Use the tables with a picture to find each of these following probabilities for thermometer readings that have a mean of 0 and s = 1. Give answers rounded to 4 decimal places.
a) between 0 and 1.5 b) between (–1.96) and 0
c) less than (-1.79) d) greater than 2.05
e) between 0.50 and 1.50
12) Use your calculator (normalcdf) to each of the following probabilities for the thermometer readings that have a mean of 0 and s = 1. Give answers rounded to 4 decimal places.
a) between (-2.00) and (-1.00) b) less than 1.62
c) greater than (-0.27) d) between (-1.08) and 0.33
e) greater than 0
13) Mean = 0 and s = 1. Find the indicated probabilities: (to 4 places)
a) P(-1.96< z < 1.96) b) P(z > -2.575)
c) P(z < 1.05) d) P( -2.34 < z < -1.67)
14) The mean for women’s weights is 143 pounds and the standard deviation is 29 pounds. Find the following probabilities to 4 places:
a) P(143 < x < 172) b) P(110 < x < 130)
c) P( x < 150) d) P( x > 150)
15) Women’s heights have a mean of 63.6 inches and s = 2.5 inches. To be a Rockette, a woman must be between 65.5 inches and 68.0 inches. If a woman is randomly selected, find the probability that she meets the height requirement.
16) SAT scores of females have a mean of 998 and s = 202. A college has a minimum of 900 as one of its requirements for admission. What percentage of females do NOT satisfy this requirement?
17) The mean is 0 and s = 1. Find the following percentiles, and round to the appropriate hundredth.
a) 10th percentile b) 25th percentile
c) 60th percentile d) 85th percentile
18) The mean for men’s heights is 69.0 inches and s = 2.8 inches. Find the following heights to the appropriate tenth of an inch:
a) 10th percentile b) 35th percentile
c) 70th percentile d) 95th percentile.
19) A test has a mean of 75 and s = 8. Find the following percentiles and round to the appropriate whole number grade:
a) 20th percentile b) 45th percentile
c) 65th percentile d) 90th percentile
20) SAT scores overall have a mean of 1017 and s = 207. If a college wants to admit only the top 30% of those, what score would they use as the minimum required? (Round to the appropriate whole number score).