Statistics and Probability Answers

QUESTION 21

Let X represent the number of children in a randomly selected South African household. The

probability distribution of X is given below.

x 1 2 3 4 5

P .x/ 0:25 0:33 0:17 0:15 0:10

(a) What is the probability that a randomly selected South African household will have more than

2 children? (3)

(b) What is the probability that a randomly selected South African household will have between

2 and 4 children (inclusive)? (3)

(c) What is the probability that a randomly selected South African household will have fewer than

4 children? (3)

(d) Calculate the expected number of children in a randomly selected South African household.

(4)

(e) Calculate the variance of the number of children in a randomly selected South African house-

hold. (5)

[18]

The regular price for a pair of shoes is $245. They are currently on sale for 25% off.  The harmonized sales tax in Ontario is 13%. Your receipt shows that the final cost is $ 215.32. Are you happy with the final cost? Explain why or why not.  Complete without a calculator and show your work.

The time taken to complete a particular type of job is distributed approximately normally with mean 1.8 hours and standard deviation 0.1 hours. (a) If normal-time work finishes at 6.00 p.m. and a job is started at 4.00 p.m., what is the probability that the job will need overtime payments? (b) What estimated completion time (to the nearest minute) should be set so that there is a 90% chance that the job is completed on time?

1)A cab driver knows from experience that the number of fares he will pick up in an evening is a random variable with µ = 21.3 and s = 3.4 Assuming that the distribution of this random variable can be approximated closely with a normal curve, find the probabilities that in an evening the driver will pick up (a) at least 30 fares (b) anywhere from 20 to 25 fares inclusively. 

Consider all possible samples of size 2 that can be drawn with replacement from the population 1, 5, and 8. Compute the following:

1. Population mean

2. Population variance

3. Population standard deviation

4. Illustrate the probability histogram of the sampling distribution of the means

Consider all possible samples of size 3 that can be drawn without replacement from the population 1, 5, and 8, 6, 10. Compute the following:

1. Population mean

2. Population variance

3. Population standard deviation

4. Illustrate the probability histogram of the sampling distribution of the means

1. A supermarket owner believes that the

mean income of its customers is P50,000

per month. One - hundred customers are

randomly selected and asked of thei r

monthly income. The sample mean is

P48,500 per month and the standard

deviation is P3,200. Is there sufficient

evidence to indicate that the mean

income of the customers of the

superma rket is P50,000 per month? Use

�� = 0.05.

The average age of public jeepneys playing in Metro Manila is 15 years. Assume that the standard deviation is 4 years. If a random sample of 64 public jeepneys is chosen, find the probability that the mean of jeepneys ages is Between 12 to 19 years

The final exam in statistics class were normally distributed with a mean of 63 and standard deviation of 5. Find the 90th percentile

As urvey unofficially claimed that in every five young executives, only one practices good reading habits.

What is the probability that out of 10 young executives, two executives practice good reading habits? （b) What is the probability that at least five out of 20 young executives practice good reading habits?