Question

In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 69.7 inches and a standard deviation of 2.0 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
. 0094. ​(Round to four decimal places as​ needed.)
​(b) Find the probability that a study participant has a height that is between 65 and 70 inches.
The probability that the study participant selected at random is between 65 and 70 inches tall is
nothing. ​(Round to four decimal places as​ needed.)
​(c) Find the probability that a study participant has a height that is more than 70 inches.
The probability that the study participant selected at random is more than 70 inches tall is

Answer 1

Solution :

Given that,

mean = = 69.7

standard deviation = =2.0

a ) P( x < 65 )

P ( x - / ) < ( 65 - 69.7 / 2.0 )

P ( z < -4.7/ 2.0 )

P ( z < - 2. 35)

Using z table

= 0.0188

Probability = 0.0188

b ) P(65 < x < 70 )

P ( 65 - 69.7 / 2.0 ) <( x - / ) < ( 70 - 69.7 / 2.0 )

P (-4.7/ 2.0 < z < 0.3/ 2.0 )

P (- 2.35 < z < 0.15 )

P ( z < 0.15 ) - P ( z < - 2.35)

Using z table

=0.8808 - 0.0188

= 8620

Probability = 0.8620

c ) P(x > 70 )

= 1 P(x < 70 )

= 1 - P ( x - / ) < ( 70 - 69.7 / 2.0 )

= 1 - P (z < 0.3/ 2.0 )

= 1 - P ( z < 0.15 )

Using z table

= 1 - 0.8808

= 0.1192

Probability = 0.1192