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

1510251240

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(drawing a spade giving that the card is black).

(c)P(drawing a diamond or black).

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

(e)P(drawing a 10/ black).

Subject: Code: Semester: (Question 3) On average, 5 traffic accidents per month occur at a certain intersection. What is the probability that in any given month, at this intersection (a) fewer than 6 accidents will occur? (b) at least 3 accidents will occur? (Question 4) A fair coin is tossed seven times. What is the probability of obtaining five tails? Name: ID: SignatureConsider the total returns between Southeast Utilities and Precision Instruments for the different market trends. The summary statistics for these two stocks are as follows: POSSIBLE PROBABILITY RETURNS OUTCOMES SOUTHEAST PRECISION Bullish Trend 0.25 1396 169% Normal Trend 0.50 5% 119% Recession 0.25 (7)96 13% Calculate the risk for both the company's stock and comment which is better and less risky?Question 8) Binomial Probability Distribution According the center for statistical research at the United Nations, 20%% on U.S. teens enjoy taking mathematics classes. Suppose 10 U.5. teens are selected and the number who enjoys taking statistics is recorded. . [5 Points] What is the probability that exactly 2 will enjoy taking statistics? . [7 Points] What is the probability that 2 or fewer will enjoy taking statistics? . [3 Points] What is the probability that 3 or more will enjoy taking statistics?The following is the list of MAD statistics for each of the models you have estimated from time-series data: Model MAD Linear Trend 238 Quadratic Trend 3.32 Exponential Trend 4.39 AR(2) 271 Based on the MAD criterion, the most appropriate model is Question 3 options: linear trend. quadradic trend. exponential trend. AR(2)