Question

Workers employed in a large service industry have an average wage of $9.00 per hour with a standard deviation of $0.50. The industry has 64 workers of a certain ethnic group. These workers have an average wage of $8.85 per hour. Calculate the probability of obtaining a sample mean less than or equal to $8.85 per hour. (Round your answer to four decimal places.)

Answer 1

The probability of obtaining a sample mean less than or equal to $8.85 per hour=0.0082

Explanation:

We are given that

Average wage,
`\mu=`$9.00/hour

Standard deviation,
`\sigma=`$0.50

n=64

We have to find the probability of obtaining a sample mean less than or equal to $8.85 per hour.

`P(\bar{x} \leq 8.85)=P(Z\leq \frac{\bar{x}-\mu}{(\sigma)/(√(n))})`

Using the values

`P(\bar{x}\leq 8.85)=P(Z\leq (8.85-9)/((0.50)/(√(64))))`

`P(\bar{x}\leq 8.85)=P(Z\leq (-0.15)/((0.50)/(8)))`

`P(\bar{x}\leq 8.85)=P(Z\leq -2.4)`

`P(\bar{x}\leq 8.85)=0.0082`

Hence, the probability of obtaining a sample mean less than or equal to $8.85 per hour=0.0082