Question

2. The speeds of cars on the highway have a mean of 65 mph with a standard deviation of 5 mph.

a) What percentage of cars averaged less than 62mph?

Answer 1

• a) 27.43%

Step-by-step explanation:

To find the percentage of cars averaged less than 62 mph calculate the corresponding z-score and use a standard normal cumulative probability table

1. Z-score

`Z-score=(x-\mu)/(\sigma)`

• x is the specific value of the random variable: 62mph

• μ is the mean of the population: 65mph

• σ is the standard deviation of the population: 5mph

Substitute and calculate

`Z-score=(62-65)/(5)=-0.600`

2. Use of the table.

The percentage of cars that averaged less than 62mph is given by the area under the curve to the left of z = -0.600.

From a standard normal cumulative probability table, the probability of z being less than -0.600 (which is equal to the probability of z being greater than 0.600) is 0.2743, which is 27.43%.

Thus, the conclusion is that 27.43% of the cars averaged less than 62mph.