(2) Women have head circumferences that are normally distributed with a mean of 22.7 in. and a standard deviation of 0.8 in. (Note: The following work is required For part (a) and (b) of this problem, (i) sketch a normal curve (ii) label the mean and any specific x value(s) with proper scales and (iii) shade the region representing the desired/given probability) (a) If the hats by Leko company produces women's hats that fit head circumferences over 23 in, what percentage of women can fit into these hats? (b) If 64 women are randomly selected, what is the probability that their mean head circumference over 23.00 in.? Low (c) If the probability in part (b) is high, does it suggest that an order for 64 hats of size lower than 23 in. will very likely fit each of 64 randomly selected women? Why or why not?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 34CR
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(2) Women have head circumferences that are normally distributed with a mean of 22.7 in. and a standard
deviation of 0.8 in.
(Note: The following work is required For part (a) and (b) of this problem,
(i) sketch a normal curve
(ii) label the mean and any specific x value(s) with proper scales and
(iii) shade the region representing the desired/given probability)
(a) If the hats by Leko company produces women's hats that fit head circumferences over 23 in,
what percentage of women can fit into these hats?
(b) If 64 women are randomly selected, what is the probability that their mean head circumference
over 23.00 in.?
Low
(c) If the probability in part (b) is high, does it suggest that an order for 64 hats of size lower
than 23 in. will very likely fit each of 64 randomly selected women? Why or why not?
Transcribed Image Text:(2) Women have head circumferences that are normally distributed with a mean of 22.7 in. and a standard deviation of 0.8 in. (Note: The following work is required For part (a) and (b) of this problem, (i) sketch a normal curve (ii) label the mean and any specific x value(s) with proper scales and (iii) shade the region representing the desired/given probability) (a) If the hats by Leko company produces women's hats that fit head circumferences over 23 in, what percentage of women can fit into these hats? (b) If 64 women are randomly selected, what is the probability that their mean head circumference over 23.00 in.? Low (c) If the probability in part (b) is high, does it suggest that an order for 64 hats of size lower than 23 in. will very likely fit each of 64 randomly selected women? Why or why not?
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