QUESTION 1.The Central Limit Theorem says: the shape of the distribution of the

Question

QUESTION 1.The Central Limit Theorem says: the shape of the distribution of the sample mean becomes approximately normal as the sample size N increases, regardless of the shape of the population.

(a) True

(b) False

QUESTION 2. From our lecture this week, we know that the weights of Pennies minuted after 1982 are approximately normally distributed with mean 2.45 grams and standard deviation of 0.02 grams. If we obtained 200 simple random samples of size N = 100 we could say the distribution of the sample means is normal with:

(a) True

(b) False

QUESTION 3. From our lecture this week, we know that the weights of Pennies minuted after 1982 are approximately normally distributed with mean 2.45 grams and standard deviation of 0.02 grams. If we obtained 1000 simple random samples of size N = 25 we could say the distribution of the sample means is normal with:

and Standard Error Equal to what?

QUESTION 4. From the lecture this week:

Suppose that the mean time for an oil change at '10-minute oil change joint' is 11.4 minutes with a standard deviation of 3.2 minutes.

If a random sample of 25 oil changes is selected, what is the mean of the sampling distribution of the sample mean??

QUESTION 5. From the lecture this week:

Suppose that the mean time for an oil change at '10-minute oil change joint' is 11.4 minutes with a standard deviation of 3.2 minutes.

If a random sample of 25 oil changes is selected, what is the standard error of the sampling distribution of the sample mean??

QUESTION 6.Suppose that the mean time for an oil change at '10-minute oil change joint' is 11.4 minutes with a standard deviation of 3.2 minutes.

If a random sample of 25 oil changes is selected, what is the probability the mean time will be great than 12 minutes?

Hint: you'll need to use the Standard Normal Table and Z-Score here.

0.8264

0.1736

0.7275

Not enough information to solve.

QUESTION 7.Suppose that the mean time for an oil change at '10-minute oil change joint' is 11.4 minutes with a standard deviation of 3.2 minutes.

If a random sample of 36 oil changes is selected, what is the probability the mean time will be great than 12 minutes?

Hint: you'll need to use the Standard Normal Table and Z-Score here. Also, notice the sample size changes to 36! Depending on how you round the standard error your result might be slightly different than the values below. Select the value closest to your solution.

1.13

0.8708

0.1292

Not enough information to answer.

QUESTION 8.Suppose that the mean time for an oil change at '10-minute oil change joint' is 11.4 minutes with a standard deviation of 3.2 minutes.

If a random sample of 25 oil changes is selected, what is the probability the mean time will be great than 10 minutes?

Hint: you'll need to use the Standard Normal Table and Z-Score here. Also, notice the sample size is 25!

0.0143

(0.9857

0.7500

-2.19

(c)

Explanation / Answer

Q8)

mean = 11.4

standard deviation = 3.2

sample size i.e n= 25

standard deviation of sample mean = standard deviation/n

= 3.2/25 = 3.2/5 = 0.64

z value = (x-mean)/sd

z value for sample mean = 10 is (10-11.4)/0.64 = -2.1875, corresponding p value using z table is 0.0143

so P(sample mean <=10) = 0.0143

P(sample mean > 10) = 1- P(sample mean <=10) = 1- 0.0143

= 0.9857

so answer is (b)

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