# Statistics: Normal Distribution and Confidence Interval

**Topics:**Normal distribution, Standard deviation, Arithmetic mean

**Pages:**13 (1734 words)

**Published:**June 17, 2011

ESSAY. Write your answer in the space provided or on a separate sheet of paper. 1)

The average score of all pro golfers for a particular course has a mean of 70 and a standard deviation of 3.0. Suppose 36 golfers played the course today. Find the probability that the average score of the 36 golfers exceeded 71.

2)

At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be between 0.99 and 1.01 centimeters?

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 3)

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. What percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?

3)

_______

A)

84%

B)

67%

C)

16%

D)

29%

4)

The standard error of the mean for a sample of 100 is 30. In order to cut the standard error of the mean to 15, we would

4)

_______

A)

increase the sample size to 200.

B)

decrease the sample to 25.

C)

decrease the sample size to 50.

D)

increase the sample size to 400.

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 5)

True or False: If the amount of gasoline purchased per car at a large service station has a population mean of $15 and a population standard deviation of $4 and it is assumed that the amount of gasoline purchased per car is symmetric, there is approximately a 68.26% chance that a random sample of 16 cars will have a sample mean between $14 and $16.

5)

_______

6)

True or False: If the amount of gasoline purchased per car at a large service station has a population mean of $15 and a population standard deviation of $4 and a random sample of 64 cars is selected, there is approximately a 95.44% chance that the sample mean will be between $14 and $16.

6)

_______

ESSAY. Write your answer in the space provided or on a separate sheet of paper. 7)

The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with μ = 110 grams and σ = 25 grams. A sample of 25 vitamins is to be selected. What is the probability that the sample mean will be between 100 and 120 grams?

8)

The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with μ = 110 grams and σ = 25 grams. A sample of 25 vitamins is to be selected. What is the probability that the sample mean will be less than 100 grams?

9)

The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with μ = 110 grams and σ = 25 grams. A sample of 25 vitamins is to be selected. What is the probability that the sample mean will be greater than 100 grams?

10)

The amount of pyridoxine (in grams) per multiple vitamin is normally distributed with μ = 110 grams and σ = 25 grams. A sample of 25 vitamins is to be selected. So, 95% of all sample means will be greater than how many grams?

TABLE 7-1

Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students.

11)

Referring to Table 7-1, what is the probability that the sample mean exceeds the population mean by more than 2 hours?

12)

Referring to Table 7-1, what is the probability that the sample mean is more than 3 hours below the population mean?

13)

Referring to Table 7-1, what is the probability that the sample mean differs from the population...

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