1. Find the sample mean x, median, variance s2, and standard deviation s of the following data:

15 10 25 12 40

2. Compute a 95% confidence interval for the true population mean if the sample mean x =15.3 cm with a sample size of10 ceramic vessels and a sample standard deviation s = 3.5 cm of ceramics vessels.

3. Let be normally distributed with a mean of 120 and standard deviation of 25.

(a) What is the Probability that X will be less than 160.

(b) Suppose a sample of 26 students were selected, what is the probability that X will be greater than 125.

4. The average body temperature of a healthy adult is = 98.6 (in degrees Fahrenheit). Jenny is concerned that her temperature is elevated, and so she took her temperature on 5 randomly chosen occasions. Her average temperature x was 99.3. Let be a random variable that represents Jenny's body temperature. You may assume that has a normal distribution with standard deviation = 0.73. Test, at the 1% level of significance, whether the sample result provides strong evidence that Jenny's body temperature of = 98.6 is elevated.

5. A recent poll of students in a certain college revealed the following information about their class scheduling:

STUDENTS

HISTORY

MATHEMATICS

BIOLOGY

TOTALS

FRESHMAN

20

45

5

70

JUNIOR

25

35

30

90

SENIOR

10

15

15

40

TOTALS

55

95

50

200

A student is selected at random, and the following variables are defined:

B: Biology, H: History, M: Mathematics, F: Freshman, J: Junior, S: Senior.

Find these probabilities:

(a) P(S/B) (b) P ( J and M) (c) P(S or M) (d) P(B /S )

6. A coin is tossed 10 times.

(a) Find the probability of getting exactly 8 heads.

(Use the Binomial Probability Distribution table)

(b) Find the probability of getting at least 8 heads.

(c) Find the expected value ' '

(d) Find the standard deviation

7. An animal shelter has a 65% adoption rate for puppies. Of all the puppies in the shelter, 71% live to be 7 years older. Of all the puppies who lived to be 7 years older, 85% were adopted,

(a) What is the probability that a random selected puppy in the shelter will get adopted and lived 7 years older?

(b) Professor Jackson is in charge of a program to prepare people for a high school equivalency exam. Records show that 4.23% of the students need work in Math, 3.14% need work in English, and 2.03% need work in both areas. Compute the probability that a student selected at random needs Math or English.

8. A pair of dice is rolled, find these probabilities:

(a) P(sum is greater or equal to 10)

(b) P(sum is less than 6 )

(c) P(sum is 8 or 12 )

(d) P(sum is at most 5)

9. Draw the Normal Distribution Curve over the indicated area given and find these probabilities:

(a) Area between Z = -2.23 and Z = 2.33,

(b) Area to the right of Z - 3.45

10. From a deck of cards, a card is drawn. Find these probabilities:

(a) P(drawing a jack and red).

(b) P(drawi

QUESTION 2 The Central Limit Theorem is important in statistics because: For any sample size, it says the sampling distribution of the sample mean is exactly normal. For any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size. For any sample size, it says the sampling distribution of the sample mean is approximately normal. For a large n, it says the population is approximately normal. For a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the population.1|.I"|.lhenetl'er a sampled populatio is normally distributed or whenever the conditions of the central limit theorem are fulfilled, the sample mean 3. bar a. is a consistent estimator of the population mean Fl? , because the mean of the sampling distribution of the sample mean equals F b. is an efcient estimator ofthe population mean i\"? , because the mean of the sampling distribution of the sample mean equals i\"? c. is an unbiased estimator of the population mean i\"? _ because the mean of the sampling distribution of the sample mean equals 3\"? d. is an efcient estimator ofthe population mean i\"? , because the mean of the sampling distribution of the sample proportion equals p at: The Central Limit Theorem is important in statistics because Question 5 options: I for a large n, it says the population is approximately normal. for any population, it says the sampling distribution ofthe sample mean is approximately normal, regardless of the sample size. for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population. for any sized sample, it says the sampling distribution ofthe sample mean is approximately normal. Suppose that the time between consecutive arrivals at an emergencyr room in a hospital has a stroneg rigl'rt skewed distribution. If a healthcare analyst is interested in estimating the mean time between arrivals, which of the following is true regarding the sampling distribution ofthe sample mean?I [pick one] 1 The sampling distribution of the sample mean will be approximately standard normal for large sample sizes 2 The sampling distribution of the sample mean will be approximately normal for small sample sizes. 3 The sampling distribution of the sample mean will be exactlyr normal for large sample sizes. 4 The sampling distribution of the sample mean will be approximater normal for large sample sizes