Statistics and Probability Answers

A couple is planning to have three children.What is the probability that?

Three marbles are in a jar—one white, one blue and one green. Two marbles are picked one at a time with replacement. Let X be the number of blue marbles picked. Construct the probability distribution.

The grade appeals process at a university requires that a jury be structured by selecting six individuals randomly from a proof of seven students and six faculty. A) what is the probability of selecting a jury of all faculty? B) what is the probability of selecting a jury of three students and three faculty ?

1.      The height of grade 1 pupils is approximately normally distributed with µ = 45 inches and s = 2. a.      If a pupil is selected at random, what is the probability that is taller than 46 inches?

4. The height of grade 1 pupils are approximately normally distributed with µ = 45 inches and  = 2. a.      A class of 30 of these pupils is used as a sample. What is the probability that the class mean is between 42 and 47?

the time for a major exam to be completed is normally distributed with an average of 55 minutes and a standard deviation of 9 minutes. If 92% of the student completed the exam, when should the test be terminated?

Q2(a) Suppose there are 8 multiple choices questions in a Statistics test. Each question has 5 possible

answers, and only one of them is correct. Find the probability of having at least 7 correct answers if a

student attempts to answer every question at random. (3 marks)

(b) Suppose that the number of patients admitted into Hospital K in an hour follows a Poisson distribution

with a mean of 5. What is the probability that more than 4 patients admitted into Hospital K in a given

30-minute interval? (4 marks)

(c) A batch of 2-cm nails are produced, where the lengths of 2-cm nails are normally distributed with a

mean of 2.0 cm and a standard deviation of 0.05 cm. The nails that are either shorter than 1.9 cm or

longer than 2.1 cm are unusable.

(i) Find the probability of all nails produced by this machine which are unusable. (4 marks)

(ii) Find k such that 80% of the nails will have the length more than k cm. (3 marks)

(d) In a 1000 replacement parts for a given assembly, 15% of the replacement parts are defective. Out of

these 1000 parts, 60% were made by the company itself, and the rest were bought from external

sources. Of those bought from external sources, 85% are good.

(i) Draw a well- labelled probability tree diagram with the joint probabilities calculated to

illustrate this situation. (5 marks)

(ii) If a part is randomly selected from this stock, what is the probability that

(1) the part is either bought or defective; (3 marks)

(2) the part is company made, given that it is good. (3 marks)

the time taken by students to solve a computer assignment produces a normal distribution with a mean of 33.0 minutes and standard deviation of 5.0 minutes. if a random sample is selected, find the probability that the student will solve:

a) in 19.1 to 28.2 minutes

b) less than 27.5 minutes

c) more than 35 minutes

coefficient of variation