A survey was conducted among 92 men and 217 women and got theirBMI values. Among the 92 men, the average BMI is 24.4 with standarddeviation 3.4. Among the 217 women, the average BMI is 22.3 andstandard deviation is 3.6.
(1) Assuming that BMI follows a normal distribution, pleasecalculate what values of BMI that the 95% of men and women willhave. In other words, 95% of men and women’s BMI will be withinwhat range. Please calculate for men and women separately. (4points)
(2) Assume that women’s BMI follows a normal distribution withthe population mean as 22 and standard deviation as 3, pleasecalculate the probability of a woman with BMI < 25, between 25–29.9, and 30 or more. (6 points)
(3) Assuming that BMI follows a normal distribution, using thesample mean, standard deviation and sample size from the sample tocalculate the 95% confidence interval for men and women’s BMIseparately. In other words, 95% of sample means of men and women’sBMI will be within what range. Please calculate for men and womenseparately. (4 points)
