Question

The time is takes a police department to arrive at the scene of a crime is normally distributed with a mean of 4.5 minutes and a standard deviation of 0.8 minutes. What percent of time will the police take 4 minutes or less to arrive? Calculate the z-score, and use the table on page 447 of the textbook

Answer 1

Given:

`Mean\text{ }\mu\text{ =4.5, standard deviation }\sigma\text{ =0.8, and x =4.}`

Required:

We need to find the percentage of the time will the police take 4 minutes or less to arrive.

Step-by-step explanation:

Consider the z-score formula.

`z=(x-\mu)/(\sigma)`

`Substitute\text{ }\mu\text{ =4.5, }\sigma\text{ =0.8, and x =4 in the formula.}`
`z=(4-4.5)/(0.8)`
`z=-0.625`

P-value from Z-Table

`P(x<4)=0.26599`

Multiply by 100 to find the percentage.

`P(x<4)\text{ \%}=0.26599*100`
`P(x<4)\text{ \%}=26.599\text{ \%}`
`P(x<4)\text{ \%}=27\text{ \%}`

Final answer:

27 % of the time will the police take 4 minutes or less to arrive.