Question

The mean weight of 1-year-old girls is 80 pounds, and the standard deviation is 6 pounds. If a sample of 31 girls is selected, what is the probability that their sample mean is between 76.5 and 81.5 pounds? Use your graphing calculator to determine this probability. Enter this answer as a number rounded to four digits after the decimal point.

Answer 1

Solution:

Given:The mean weight of 1-year-old girls is 80 pounds, and the standard deviation is 6 pounds.

Sample size = n = 31

Find:

Since sample size n = 31 is large , we can use Central limit theorem which states that for large sample size n ,
sampling distribution of sample mean is approximately normal with mean of sample means:

and standard deviation of sample means is:

Now use following steps in TI 84 plus calculator:

Press 2ND and VARS

Select normalcdf(

Enter numbers

Click on Paste and press Enter two times.

Thus