Question

Women have head circumferences that are normally distributed with a mean given by ​u= 23.76in, and a standard deviation given by o= 1.1in.

a. If a hat company produces​ women's hats so that they fit head circumferences between 23.1 in. and 24.1 ​in., what is the probability that a randomly selected woman will be able to fit into one of these​ hats? The probability is . 4165. ​(Round to four decimal places as​ needed.)

Answer 1

Sol:

sample mean=xbar=mu=23.76

sample standard deviation=sigma/sqrt(n)=1.1/sqrt(1)=1.1

xbar follows approximately normal distribution with

xbar~N(23.76,1.1)

need to find

P(23.1<xbar<24.1)

need to convert z scores as

z=x-mean/sd

P(23.1-23.76/1.1<Z<24.1-23.76/1.1)

P(-0.6<Z<0.3090909)

P(z<0.3090909)-P(Z<-0.6)

0.6214-0.2743

=0.3471

answer is 0.3471,it cannot be 0.4165.check