In this question, use Excel functions rather than Normal distribution tables.

The number of new cars sold by "Ma's New Car Factory" in a financial year can be approximated by a normal distribution with a mean of 125,000 cars and a standard deviation of 34,000 cars.
Part A
In order to recover all costs associated with manufacture they need to sell 100,000 cars. What is the probability that "Ma's New Car Factory" will do better than just covering their costs if the sales are distributed as expected? Give your answer to two decimal places in the form x.xx.

Part B
What is the number of cars sales that the company has a only a 10% chance of achieving next year? Give you answer as a whole number.

A.0.23

To solve this problem using Excel functions, we can use the `NORM.DIST` function to calculate the probability and the `NORM.INV` function to find the number of car sales.

Part A:

To find the probability that "Ma's New Car Factory" will do better than just covering their costs (selling more than 100,000 cars), we can subtract the cumulative probability of selling exactly 100,000 cars from 1.

1. Open Excel and enter the mean and standard deviation in separate cells. Let's assume the mean (average) is in cell A1 and the standard deviation is in cell B1.
2. In another cell, let's say cell C1, use the following formula: `=1- NORM.DIST(100000,A1,B1,TRUE)`
- The NORM.DIST function takes four arguments: the value for which you want to calculate the probability, the mean, the standard deviation, and TRUE to specify that you want the cumulative probability.
- In this case, we specify 100,000 cars as the value for which we want to calculate the probability.
3. Press Enter to get the result.
4. Format the result as a percentage with two decimal places.

The result in cell C1 will give you the probability that "Ma's New Car Factory" will do better than just covering their costs.

Part B:

To find the number of car sales that the company has a 10% chance of achieving, we can use the `NORM.INV` function.

1. In a new cell, let's say cell D1, use the following formula: `=NORM.INV(0.1,A1,B1)`
- The NORM.INV function takes three arguments: the probability, the mean, and the standard deviation.
- In this case, we specify 0.1 (10%) as the probability.
2. Press Enter to get the result.
3. Format the result as a whole number (no decimal places).

The result in cell D1 will give you the number of car sales that the company has a 10% chance of achieving.

Note: Make sure to adjust the cell references based on where you have entered the mean and standard deviation in your Excel worksheet.

A. Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.

B. Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.10) to find the Z score. Insert Z value into equation above.

A. 8.95