Question

According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 68 inches and a standard deviation of 2.5 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places According to a study done by UCB s% of Martian heights lie between what two numbers? Low: __inches High: ___inches must be 4 decimals rounded

Answer 1

Here we take s=90,95,99 (since s is not given)

z_0.05=1.6449 (Use R code: round(qnorm(0.95),4)),

z_0.025=1.959964 (Use R code: round(qnorm(0.975),6)),

z_0.005=2.5758 (Use R code: round(qnorm(0.995),4)).

90% of Martian heights lie between what two numbers:

Low: 68-z_0.05*2.5=68-1.6449*2.5=63.8878 inches; High: 68+z_0.05*2.5=68+1.6449*2.5=72.1123.

95% of Martian heights lie between what two numbers:

Low: 68-z_0.025*2.5=68-1.959964*2.5=63.1001 inches; High: 68+z_0.025*2.5=68+1.959964*2.5=72.8999.

99% of Martian heights lie between what two numbers:

Low: 68-z_0.005*2.5=68-2.5758*2.5=61.5605 inches; High: 68+z_0.005*2.5=68+2.5758*2.5=74.4395.