Question

The amounts of time per workout an athlete uses a stair climber are normally​ distributed, with a mean of 21 minutes and a standard deviation of 5 minutes. Find the probability that a randomly selected athlete uses a stair climber for​

(a) less than 17 ​minutes,

(b) between 21 and 28 ​minutes, and​

(c) more than 30 minutes.

Answer 1

Solution :

Given that,

mean = = 21

standard deviation = =5   

P(X< 17) = P[(X- ) / < (17-21) /5 ]

= P(z < -0.8)

Using z table

= 0.2119

B.

P(21< x < 28) = P[(21 - 21) /5 < (x - ) / < (28 - 21) /5 )]

= P(0< Z < 1.4)

= P(Z <1.4 ) - P(Z < 0)

Using z table   

= 0.9192-0.5

probability= 0.4192

C.

P(X<30 17) = 1 -P[(X- ) / < (30-21) /5 ]

=1 - P(z < 1.8)

Using z table

= 1 - 0.9641

=0.0359