Question

Suppose the life span of a calculator has a normal distribution with a mean of 60 months and a standard deviation of 8 months. What is the probability that the calculator works properly for 74 months or more

Answer 1

Answer:

Probability that the calculator works properly for 74 months or more is 0.04 or 4%.

Step-by-step explanation:

We are given that the life span of a calculator has a normal distribution with a mean of 60 months and a standard deviation of 8 months.

Firstly, Let X = life span of a calculator

The z score probability distribution for is given by;

         Z = $\frac{ X - \mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean = 60 months

            $\sigma$ = standard deviation = 8 months

Probability that the calculator works properly for 74 months or more is given by = P(X $\geq$ 74 months)

     P(X $\geq$ 74) = P( $\frac{ X - \mu}{\sigma}$ $\geq$ $\frac{74-60}{8}$ ) = P(Z $\geq$ 1.75) = 1 - P(Z < 1.75)

                                                   = 1 - 0.95994 = 0.04

Therefore, probability that the calculator works properly for 74 months or more is 0.04 or 4%.