Chapter 7, Section 7.2,Question E32 The heights of males in a population are app
ID: 2947093 • Letter: C
Question
Chapter 7, Section 7.2,Question E32 The heights of males in a population are approximately normally distributed with mean 69.3 inches and standard deviation 2.92. The heights of females in the same population are approximately normally distributed with mean 64.1 inches and standard deviation 2.75 a. Suppose one male from this age group is selected at random and one female is independently selected at random and their heights added. Find the mean and standard error of the sampling distribution of this sum. Mean Standard deviation (round to three decimal places) b. Find the probability that the sum of the heights is less than 125 inches (round to four decimal places) c. What total heights are reasonably likely? (round to two decimal places) d. What is the probability that the male is at least 2 inches taller than the female? (round to four decimal places) By accessing this Question Assistance, you will learn while you earn points based on the Point Potential Policy set by your instructor.Explanation / Answer
Solution :
Given that for males mean ?x = 69.3 , standard deviation ?x = 2.92
for females mean ?y = 64.1 , standard deviation ?y = 2.75
a. mean ? = ?x + ?y = 69.3 + 64.1 = 133.4
standard deviation ? = sqrt(?x^2 + ?y^2) = sqrt(2.92^2 + 2.75^2) = 4.011
b. P(sum < 125) = P((sum - ?)/? < (125 - 133.4)/4.011)
= P(Z < -2.0942)
= 0.0183
c. I'm assuming by "reasonably likely" it's asking for "within 2 standard deviations of the mean.
=> Mean +/- 2*SD = 133.4 +/- 2*4.011
=> (125.38 , 141.42)
d. mean ? = 69.3 - 64.1 = 5.2
standard deviation ? = 4.011
P(x >= 2) = P((x - ?)/? >= (2 - 5.2)/4.011)
= P(Z >= -0.7978)
= 0.7881