Decision making process

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).

3 - Normal Distributions and Probability LEARNING OBJECTIVE: Identify the probability of values below the mean in a standard distribution curve. Based on the shaded area in this normal distribution, Grant's Bakery lies in the top percent of all local businesses when considering how long they've been in business. 2 Grant's BakeryLet X have a normal distribution with parameters u=171 and o=15. Find the 84th percentile approximately. Hint: Use Table A.3 to find the 84th percentile of the standard distribution then use the obtained value to compute the 84th percentile of the given normal distribution. Select one: O a. 171 O b. 186 O C. 201 O d. 216 O e. 30.04. If X; ~ Normal(0, 1), i = 1, ...,n independently and identically, find the distribution of Y = X? + X3 + X3 + ...+ X2. Identify the distribution with a standard distribution known to you, along with the appropriate parameters. Use any method/combination of methods to do this