Statistics and Probability Answers

1. A certain company makes electrical cables having a mean strength of 40 kg/cm² and a standard deviation of 2 kg/cm². Assuming the strength follows a normal distribution,

a. What percentage of cables will have a strength exceeding 43 kg/cm²?

b. If strength is measured to the nearest kg/cm², what percentage of cables will have

strength exceeding 43 kg/cm²?

c. Illustrate the normal curve for a and b.

THE PRESIDENT OF A SERVICE UTILITY CLAIMS THAT 60 PERCENT OF HIS 500,000 CUSTOMERS ARE VERY SATISFIED WITH THE SERVICE THEY RECEIVE. TO TEST THIS CLAIM, THE LOCAL NEWSPAPER SURVEYED CUSTOMERS, USING SIMPLE RANDOM SAMPLING. AMONG THE SAMPLED CUSTOMERS, 64 PERCENT SAY THEY ARE VERY SATISFIED. BASED ON THESE FINDINGS, CAN WE REJECT THE PRESIDENT'S HYPOTHESIS THAT 64% OF THE CUSTOMERS ARE VERY SATISFIED? USE A 0.01 LEVEL OF SIGNIFICANCE.

II. Determine the given of the problems below and formulate the null and alternative hypothesis both in words and symbols. Write your answer in your notebook. Please follow the format in the examples.

2. A study was conducted to determine the marrying age of teachers. It was found out that the mean marrying ager of teachers is 30 years old. Fifteen teachers were surveyed randomly and found that their mean marrying age was 33 years old with a standard deviation of 5 years. Use 10% level of significance to test the hypothesis and assume that the population is normally distributed.

3. A study was conducted to determine the marrying age of teachers. It was found out that the mean marrying ager of teachers is 30 years old. Fifteen teachers were surveyed randomly and found that their mean marrying age was 33 years old with a standard deviation of 5 years. Use 10% level of significance to test the hypothesis and assume that the population is normally distributed.

In the class of Statistics, there are 75 students in total out of which 55 male, 20 female students. 10 students need to be selected for the occasion of freshers' reception.

a. Find out the mean and standard deviation of the binomial distribution.

A MNP publisher of Statistics and Probability textbooks claims that the

average price of all hardbound textbooks is Php 500. A group of students

believes that the actual mean is higher and wishes to test their belief.

Find the area to the left of critical value t = 2.500 when sample size is 24

Three machines A, B and C produce respectively 50%, 30% and 20% of the total number of items of a factory. The percentage of defective output of these machines are 3%, 4% and 5% respectively. if an item selected at random, find the probability that the item is non-defective.

The average public elementary school has 468 students with a standard deviation of 87.If a random sample of 38 public elementary schools is selected,what is the probability that the number of students enrolled is between 445 and 485

A health specialist wants to determine the average number of hours a person

exercises in a day during the quarantine period. She found out that the mean number

of hours a person exercises in a day during the quarantine period is 80 minutes. A

random sample of 29 persons were surveyed and found that their mean is 65 minutes

and a standard deviation of 10 minutes. Test the hypothesis at 2% level of significance

and assume that the population is normally distributed.

A dart hits the circular dartboard shown below at a random point. Find the probability that the dart lands in the shaded square region. The radius of the dartboard is 9

in, and each side of the shaded region is 3in.