Question

In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 69.3 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Complete parts​ (a) through​ (d) below. ?(a) Find the probability that a study participant has a height that is less than 66 inches.The probability that the study participant selected at random is less than 66 inches tall is __

?(Round to four decimal places as? needed.)

(b) Find the probability that a study participant has a height that is between 66 and 71 inches.The probability that the study participant selected at random is between 66 and 71 inches tall is ___

?(Round to four decimal places as? needed.)

?(c) Find the probability that a study participant has a height that is more than 71 inches.The probability that the study participant selected at random is more than 71inches tall is ___

?(Round to four decimal places as? needed.)

?(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.

Answer 1

Answer:

A)The probability that the study participant selected at random is less than 66 inches tall is 0.1357

B)The probability that the study participant selected at random is between 66 and 71 inches tall is 0.152

C)The probability that the study participant selected at random is more than 71 inches tall is 0.7123

Step-by-step explanation:

$\mu = 69.3$

$\sigma = 3$

A) Find the probability that a study participant has a height that is less than 66 inches.

We are supposed to find P(x<66)

$x= 66$

$z= \frac{x-\mu}{\sigma}$

$z= \frac{66-69.3}{3}$

$z=-1.1$

Use z table :

So, P(z<-1.1)=0.1357

So, The probability that the study participant selected at random is less than 66 inches tall is 0.1357

B) Find the probability that a study participant has a height that is between 66 and 71 inches.

We are supposed to find P(66<x<71)

At x = 66

$z= \frac{x-\mu}{\sigma}$

$z= \frac{66-69.3}{3}$

$z=-1.1$

Use z table :

So, P(z<-1.1)=0.1357

At x = 71

$z= \frac{x-\mu}{\sigma}$

$z= \frac{71-69.3}{3}$

$z=0.56$

Use z table :

So, P(z<0.56)=0.2877

P(-1.1<z<0.56)=P(z<0.56)-P(z<-1.1)=0.2877-0.1357=0.152

So,The probability that the study participant selected at random is between 66 and 71 inches tall is 0.152

C)Find the probability that a study participant has a height that is more than 71 inches

We are supposed to find P(x>71)

$z= \frac{x-\mu}{\sigma}$

$z= \frac{71-69.3}{3}$

$z=0.56$

Use z table :

So, P(z<0.56)=0.2877

P(z>0.56)=1-P(z<0.56)=1-0.2877=0.7123

So,The probability that the study participant selected at random is more than 71 inches tall is 0.7123