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

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

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 =
`( 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(
`( X - \mu)/(\sigma)`
`\geq`
`(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%.