4 A manufacturer of women's clothing wants to know the mean height of the women in a town (in order to plan what proportion of garments should be of each size). She knows that the standard deviation of their heights is 5 cm. She selects a random sample of 50 women from the town and finds their mean height to be 165.2 cm. (i) Use the available information to estimate the proportion of women in the town who were (a) over 170 cm tall (b) less than 155 cm tall. (ii) Construct a 95% confidence interval for the mean height of women in the town. (iii) Another manufacturer in the same town wants to know the mean height of women in the town to within 0.5 cm with 95% confidence. What is the minimum sample size that would ensure this?
4 A manufacturer of women's clothing wants to know the mean height of the women in a town (in order to plan what proportion of garments should be of each size). She knows that the standard deviation of their heights is 5 cm. She selects a random sample of 50 women from the town and finds their mean height to be 165.2 cm. (i) Use the available information to estimate the proportion of women in the town who were (a) over 170 cm tall (b) less than 155 cm tall. (ii) Construct a 95% confidence interval for the mean height of women in the town. (iii) Another manufacturer in the same town wants to know the mean height of women in the town to within 0.5 cm with 95% confidence. What is the minimum sample size that would ensure this?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Transcribed Image Text:4 A manufacturer of women's clothing wants to know the mean height of the
women in a town (in order to plan what proportion of garments should be of
each size). She knows that the standard deviation of their heights is 5 cm. She
selects a random sample of 50 women from the town and finds their mean
height to be 165.2 cm.
(i) Use the available information to estimate the proportion of women in the
town who were
(a) over 170 cm tall
(b) less than 155 cm tall.
(ii) Construct a 95% confidence interval for the mean height of women in the
town.
(iii) Another manufacturer in the same town wants to know the mean height
of women in the town to within 0.5 cm with 95% confidence. What is the
minimum sample size that would ensure this?
Transcribed Image Text:4 (i) (а) 0.1685
(b) 0.0207
(ii) 163.8–166.6 cm
(iii) 385
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