Question

A company services home air conditioners. It is known that times for service calls follow a normal distribution with a mean of 60 minutes and a standard deviation of 10 minutes. A random sample of eight service calls is taken. What is the probability that exactly two of them take more than 68.4 minutes? For calculation convenience, you may round probability results to the nearest thousandth (3 decimals).

Answer 1

Solution :

Given that ,

mean = = 60

standard deviation = = 10

= / n = 10 / 8 = 3.5355

P( > 68.4) = 1 - P( < 68.4)

= 1 - P[( - ) / < (68.4 - 60) / 3.5355]

= 1 - P(z < 2.38)

= 1 - 0.9913

= 0.009

Probability = 0.009