Statistics and Probability Answers

From a recent survey in Cambridge University, it was discovered that 8% of the students are short-sighted.

a) If 20 students are randomly selected, calculate :

i. the probability that none of them are short-sighted

ii. the probability that at most 2 are short-sighted

iii. the standard deviation for the number of short-sighted student

b) If 50 classes of 20 students are randomly selected, what is the probability that 10 classes have no short-sighted students?

50 students selected at random from 500 students enrolled in a computer crash

programme were classified according to the age and grade points giving the

following data:

Age (in years)

Grade Point Below 20 21-30 Above 30

Up to 5 - 3 5 2

5.1 to 7.5 - 8 7 5

7.6 to 10.0 - 4 8 8

Test at 5% level of significance that age and grade points are independent

According to Nielsen Media Research, the (population) average number of hours of TV viewing per household per week in the United States is 50.4 hours. Suppose the (population) standard deviation is known to be 11.8 hours. A random sample of 42 U.S. households is taken. What is the probability that the sample mean is less than 40 hours but greater than 35 hours?

According to Nielsen Media Research, the (population) average number of hours of TV viewing per household per week in the United States is 50.4 hours. Suppose the (population) standard deviation is known to be 11.8 hours. A random sample of 42 U.S. households is taken. What is the probability that the sample mean is less than 47.5 hours?

According to Nielsen Media Research, the (population) average number of hours of TV viewing per household per week in the United States is 50.4 hours. Suppose the (population) standard deviation is known to be 11.8 hours. A random sample of 42 U.S. households is taken. What is the probability that the sample mean is more than 52 hours?

How many arrangements are possible for the word GROVEL if the vowels

are always together?

Suppose samples of size 2 are drawn from the population. List all the possible samples and the corresponding means.

Identify at least three (3) problems that will make use of multiple regression analysis. For each problem,

what are your independent variables, and what is your dependent variable? What level of measurement

that is most appropriate to measure each of the variables whether independent variables or dependent

variable?

Make a study about how many sheets of paper you consumed weekly in 

answering your Self Learning Modules. Record the quantity (total number of 

sheets) per subject, then construct a probability distribution. Compute the 

mean, variance, and the standard deviation of the probability distribution you 

made. Interpret the result, then find out how many weeks you will consume 

50 sheets of pad paper.

Observe yourself in a day. Find out how many hours you spend in the following 

activities: house chores, answering Self Learning Modules, planting/gardening, 

using social media like Facebook, messenger, tiktok, Instagram, and YouTube, 

listening to music, watching television, and sleeping. Record your data. Construct a 

probability distribution, then compute the mean (µ), variance (σ2), and standard 

deviation (σ) of the probability distribution that you made.