1 Normal distribution Suppose the average stock price for a

1 (Normal distribution) Suppose the average stock price for a company listed on the S&P 500 is 30.00 and the standard deviation of the stock price is 20.00. What is the probability a company’s stock price is between 35 and 50?

2 (Sampling distribution of sample mean) If you measure your height many times, then you may have a lot of different measurements. Suppose that a single measurement has the normal distribution with mean µ = 1.75 meters and standard deviation = 0.1 meters. Assume that you measure your height5 times and let x be the mean of the 5 measurements.

a What is the mean and standard deviation of ?

b How many times must you measure to reduce the standard deviation of to 0.03?

3 (Sampling distribution of sample mean) The foreman of a bottling plant has observed that the amount of pop in each 32-ounce bottle is actually a normally distributed random variable, with a mean of 32.2 ounces and a standard deviation of .3 ounce. If a customer buys a carton of four bottles, what is the probability that the mean amount of the four bottles will be greater than 32 ounces?

Part II. The following questions are for Excel applications

4 Suppose you are selling sandwiches. 30% of people choose chicken, the rest choose other meats. What is the probability of selling 0-6 chicken sandwiches to the next 6 customers?

The following 4 questions are corresponding to probability calculation by hand.

Show a column with formulas of probability of “x=0” to “x=6” specifically.

Create another column with results of the formulas above.

Create a new column with formulas of probability of “x0” to “x6”.

Create another column with results of probability of “x0” to “x6”

The next 2 questions are for EXCEL functions.

5 Create a column with results of probability of “x=0” to “x=6”. Write down the function with details in bracket for the 1^st cell by hand.

6 Create another column with probability of “x0” to “x6”. Also write down the function with details in bracket for the 1^st cell by hand.

Your company makes sports bikes. 80% pass final inspection (20% fail and need to be fixed). You will make 10 bikes in the next working hour, what is the probability of 0-10 bikes among them fail and need to be fixed?

7 Create a column with results of failing probability of “x=0” to “x=10”. Write down the function with details in bracket for the 1^st cell by hand.

8 Create another column with failing probability of “x0” to “x10”. Also write down the function with details in bracket for the 1^st cell by hand.

Solution