Assume that women\'s heights are normally distributed with a mean given by =62.4
ID: 3129877 • Letter: A
Question
Assume that women's heights are normally distributed with a mean given by
=62.4 in, and a standard deviation given by =1.8 in.
(a) If 1 woman is randomly selected, find the probability that her height is less than 63in.
(b) If 31 women are randomly selected, find the probability that they have a mean height less than 63in.
(a) The probability is approximately______?
(Round to four decimal places as needed.)
(b) The probability is approximately______?
(Round to four decimal places as needed.)
Can you help me set up the equation and help me solve please? I'm reading too much into this and the last response did not use the correct numbers so it really confused me! Thanks!!
Explanation / Answer
a)Using Central limit theorem the sampling distribution of sample mean is normally distributed with mean =62.4 in and standard deviation 1.8/sq rt n=1.8/1=1.8
For X=63, z=(x-)/=(63-62.4)/1=0.6
P(X<63)=P(z<0.6)=0.7257
b)Similarly, Using Central limit theorem the sampling distribution of sample mean is normally distributed with mean =62.4 in and standard deviation 1.8/sq rt n=1.8/sq rt 31=0.32
For X=63, z=(63-62.4)/0.32=1.8
P(X<63)=P(z<1.8)=0.9641