The mean height of women in a country ages 2029 is 637 inche

The mean height of women in a country (ages

2029) is 63.7 inches. A random sample of 75 women in this age group is selected. What is the probability that the mean height for the sample is greater than 64

inches? Assume sigmaequals=2.78

The probability that the mean height for the sample is greater than 64 inches is?

(Round to four decimal places as needed.)

Solution

assuming the height of women in a country of ages 20-29 follows normal distribution with mean 63.7 inches and standdard deviation=2.78

let X1,X2,.....X75 be a random sample of size n=75 from this distribution. and Xbar be tha sample mean

so X1,X2,....,X75~N(63.7,2.78²) hance Xbar~N(63.7,(2.78²)/75)

so P[Xbar>64]=P[(Xbar-63.7)/(2.78/squareroot(75))>(64-63.7)/(2.78/squareroot(75))]=P[Z>0.93456] where Z~N(0,1)

=1-P[Z<0.93456]=1-0.824992=0.175008 [answer]