Homework: Lesson 5, Section 5.2 Homework Score: 0.25 of 1 pt 5.2.7-T Save 40f 8
ID: 3364269 • Letter: H
Question
Homework: Lesson 5, Section 5.2 Homework Score: 0.25 of 1 pt 5.2.7-T Save 40f 8 (7 complete) Hw Score: 78.13%, 6.25 of 8 p EQuestion Help In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 69.8 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. rk T(a) Find the probability that a study participant has a height that is less than 65 inches. n The probability that the study participant selected at random is less than 65 inches tall is 0.0548. (Round to four decimal places as needed.) ok (b) Find the probability that a study participant has a height that is between 65 and 70 inches. ch The probability that the study participant selected at random is between 65 and 70 inches tall is(Round to four decimal places as needed.) dia Enter your answer in the answer box and then click Check Answer. Clear All Check Answer To see what to study next,go to your Study Plan 4948Explanation / Answer
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 69.8
standard Deviation ( sd )= 3
a.
P(X < 65) = (65-69.8)/3
= -4.8/3= -1.6
= P ( Z <-1.6) From Standard Normal Table
= 0.0548
b.
BETWEEN THEM
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 65) = (65-69.8)/3
= -4.8/3 = -1.6
= P ( Z <-1.6) From Standard Normal Table
= 0.0548
P(X < 70) = (70-69.8)/3
= 0.2/3 = 0.0667
= P ( Z <0.0667) From Standard Normal Table
= 0.5266
P(65 < X < 70) = 0.5266-0.0548 = 0.4718
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