Statistics and Probability Answers

A population has a mean of 500 and a standard deviation of 50. A sample of 40 will be taken and the sample mean x̄ will be used to estimate the population mean. Assume that the population is infinite.

What is the standard deviation of x̄?

a. 1.25
b. 7.91
c. 40
d. 50

An outdoor store sells 200 survival kits per month, with a population standard deviation (σ) of 15 kits. Assume the selling of survival kits is normally distributed.

What is the probability that the outdoor store will sell between 191 and 221 survival kits per month?

a. 1.4011
b. .4761
c. .9250
d. .6449

What is the probability that the outdoor store will sell more than 242 kits per month?

a. .4974
b. .0026
c. .9974
d. .8838

Given z is a standard normal random variable, answer questions 1 through 4.

1. p(z = 2.3) is

a. .1056.
b. 0.
c. .8944.
d. .3944.

2. p(z ≥ -1.84) is

a. .5474.
b. 0.
c. .0329.
d. .9671.

3. p(z ≤ 1.4) is

a. .0808.
b. .9192.
c. .9927.
d. 0.

4. p(.5 ≤ z ≤ 2.9) is

a. 0.
b. .6915.
c. .3066.
d. 9981.

The probability of Sue winning a game of darts is 0.4. If she plays 100 games how many would you expect
her to lose? (She can either win or lose. She can’t draw)

1. (a) A class has 10 boys and 5 girls. Three students are selected at random one after another. Find the probability that (i) first two are boys and third is girl (ii) first and third are of same sex and the second is of opposite sex.
(b) Two aero planes bomb a target in succession. The probability of each correctly scoring a hit is 0.3 and 0.2 respectively. The second will bomb only if the first misses the target. Find the probability that (i) target is hit (ii) both fails to score hits.

A screw manufacturer makes specialized tiny screws that are 15mm long. The manufacturing process does not make every screw exactly 15mm long. Suppose we know that the lengths of the screws have population mean 15mm and population standard deviation 0.04mm. To test for quality control, 100 screws are to be measured. What is the distribution of the sample means for samples of size 100?

A,B,C,D cut a pack of 52 cards successively in the order given. If a person who cuts a spade first receives rs.700, what are their respective expectations?

What are 3 types of statistical analysis or tools that could be used in the task of a major hotel chain to offer an incentative program. And how it be used in this situation?

How can Satatistics and probability be used in a major hotel chain for offering an incentive program for guests?

Kellogg’s marketing department conducts an experiment to find out whether consumers can distinguish between its various brands of breakfast cereal. Five very small bowls of different brands of cereal were placed in front of each of eight persons participating in the experiment. The bowls were labeled A, B, C, D and E. Each person was informed that only one bowl contained his or her favorite cereal. Suppose that none of the eight persons in the experiment was able to identify his or her favorite cereal and just guessed which bowl it was in. What is the probability that no more than two of the eight participants guessed correctly?