Question

The amount of time to complete a physical activity in a PE class is normally distributed with a mean of 37.6 seconds and a standard deviation of 5.4 seconds. Round answers to 4 decimal places.

a) What is the probability that a randomly chosen student completes the activity in less than 31.5 seconds?

b) What is the probability that a randomly chosen student completes the activity in more than 42.5 seconds?

c) What proportion of students take between 33.8 and 40.6 seconds to complete the activity?

d) 70% of all students finish the activity in less than ___ seconds.

JUST TRYING TO FIND D

Answer 1

solution:

part d

Given that,

mean =  = 37.6

standard deviation =  = 5.4

Using standard normal table,

P(Z < z) = 70%

=(Z < z) = 0.70  

= P(Z < 0.52 ) = 0.70  

z = 0.52   

Using z-score formula  

x = z +

x = 0.52 *5.4+37.6

x = 40.408 sec