Question

The time, X minutes, taken by Tim to install a satellite dish is assumed to be a normal random variable with mean 127 and standard deviation 20. Determine the probability that Tim will takes less than 150 minutes to install a satellite dish.

Answer 1

Answer: 0.8749

Explanation:

Given, The time, X minutes, taken by Tim to install a satellite dish is assumed to be a normal random variable with mean 127 and standard deviation 20.

Let x be the time taken by Tim to install a satellite dish.

Then, the probability that Tim will takes less than 150 minutes to install a satellite dish.

`P(x<150)=P(\frac{x-\text{Mean}}{\text{Standard deviation}}<(150-127)/(20))\\\\=P(z<1.15)\ \ \ [z=\frac{x-\text{Mean}}{\text{Standard deviation}}]\\\\=0.8749\ [\text{By z-table}]`

hence, the required probability is 0.8749.