Statistics and Probability Answers

Apart from being in the education sector, Richfield also has a fleet of cars available for rent. 

Statistics shows that the Mercedes AMG G63 is the most rented car among their fleet and one in four customers request this make. If 5 of today’s rentals are selected, what is the probability that 2 clients would have rented an AMG G63?

1. Given the following data, compute the mean marks and standard deviation

Class       0-25   25-50  50-75   75-100

Frequency 30 50 80 40

2. Explain the importance and application of Linear Regression in drug stability studies.

3. Perform the one-way ANOVA for the data of testing of a new drug on four patients, data is given below:

Clinic 1 2 3 4 5 6 7

Patient 1 5 7 12 9 11 6 10

Patient 2 3 7 10 8 9 9 10

Patient 3 6 7 5 7 13 9 7

Patient 4 8 11 6 5 7 12 9

If X and Y are independent r.v.s with M (t) X

 and M (t) Y

 as their m.gf’s 

respectively, then M (t) M (t)M t) true or false

If H0

: P ≤ 6.0 and X ~ B(n, p)n -known and p unknown and 1 0 H :µ = µ where 

X ~ N

2 2

(µ,σ )σ unknown, then H0

 and H1

 are simple null hypothesis.

onsider the population consisting of the values (1, 3, 8)

i. List all the possible samples of size 2 with replacement.

ii. Compute the mean of each sample.

iii. Identify the probability of each sample.

iv. Compute the mean of the sampling distribution of the means.

v. Compute the population mean.

vi. Compare the population mean with the mean of the sampling distribution of mean

Suppose that a real estate negotiator has ten potential house buyers. The negotiator believes that for each potential house buyer, the probability of making a sale is 0.50.

(a) Find the probability that the negotiator makes less than two sales.

(b) Find the probability that the negotiator makes between eight and ten sales (inclusive).

(c) Find the mean and standard deviation of sales that the negotiator will be able to make.

(d) The negotiator can use a normal approximation for this binomial distribution. Explain why this is possible.

(e) Using normal approximation, calculate the probabilities in (a) and (b). [12]

The following data describe the distribution of grades out of 20, obtained by 20 students during a quiz of Statistics: 6; 7; 5; 7; 7; 8; 7; 6; 9; 7; 4; 10; 6; 8; 8; 9; 5; 6; 4; 8.

Calculate the mean.

A population consists of the numbers 2, 4, 8, 10 and 5. Let us list all the possible samples of size 3 from this population and construct the sampling distribution of the sample mean.

A doctor examined a patient to determine the cause of a disease. He took a drop of blood

       and used it to determine the state of health of patient. What aspect of statistics is the doctor

       employing in order to form a judgment? Briefly explain why the doctor used this method?

You ask a friend to think of a number from 4 to 10. What is the probability that his number will be a multiple of three?