Question

A researcher is studying the monthly gross incomes of drivers for a ride sharing company. (Gross incomes represent the amount paid to drivers before accounting for the costs associated with driving.) The researcher obtains a list of all the drivers in San Francisco and randomly selects 200 of them to contact. The list of incomes in the sample has an average of $800 per month, with an SD of $1000. (a) Does the histogram of the sample incomes follow the normal curve? Explain why or why not.

Answer 1

Answer:

The histogram of the sample incomes will follow the normal curve.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

In this case the researches wants to determine the monthly gross incomes of drivers for a ride sharing company.

He selects a sample of n = 200 drivers and ask them their monthly salary.

As the sample selected is quite large, i.e. n = 200 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample mean by the Normal distribution.

Thus, the histogram of the sample incomes will follow the normal curve.