Question

For the 405 highway that car pass through a checkpoint, assume the speeds are normally distributed such that μ= 61 miles per hour and δ=4 miles per hour. Calculate the Z value for the next car that passes through the checkpoint will be traveling slower than 65 miles per hour.

Answer 1

`Z = 1`

Explanation:

Z - score

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

`\mu = 61, \sigma = 4`

Calculate the Z value for the next car that passes through the checkpoint will be traveling slower than 65 miles per hour.

This is Z when X = 65. So

`Z = (X - \mu)/(\sigma)`

`Z = (65 - 61)/(4)`

`Z = 1`