Question

In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 68.3 inches and a standard deviation of 4.0 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 65 inches.

The probability that the study participant selected at random is less than 65 inches tall is (......). ​(Round to four decimal places as​ needed.)

Answer 1

Given :-

Mean (M) = 68.3,

Standard deviation (sd) = 4.0

Let, X has a standard normal distribution.

Therefore ,

z = ( X - M ) / sd

Now, we have to find P( X < 65 )

Therefore,

P( X<65) = P[ ( (X-M) / sd ) < ( (65-68.3) / 4.0) ]

---- round up 3 decimal

P( X < 65 ) = P( z < -0.825 ) --- use statistical calculator

P( X < 65 ) = 0.2047

The probability that the study participant selected at random is less than 65 inches tall is 0.2047.

OR.... use z table then

P( X < 65 ) = P ( z < -0.83 )

----- round up 2 decimal

Then ,

P( X < 65 ) = 0.20333

The probability that the study participant selected at random is less than 65 inches tall 0.2033.