Statistics and Probability Answers

Osman, Sello and Danda Pvt Ltd sells maintenance agreements valid for 1 year for the refrigerators

they make. Osman, Sello and Danda has established a probability distribution of costs incurred

during the 1 year warranty period as follows:

COST PROBABILITY

R0 0:88

R2 500 0:07

R5 000 0:02

R7 500 0:02

R10 000 0:01

A washing machine company chooses a random sample of 10 motors received from one of the suppliers. It determines the length of life of each of the motors. The results (in thousands of hours) are as follows: 4.5, 5.0, 4.2, 4.8, 4.2, 5.1, 4.0, 4.2, 4.2, 4.5

Computer a point estimate of the mean length of life of the motors received from the supplier.

What are the various probability distributions, give respective formulas of each type of distribution. Now solve the problem“The probability that at least one of the two independent events occurs is 0.5. Probability thatthe first event occurs but not the second is 3/25. Also the probability that the second event occurs but not the first is 8/25.”Find the probability that none of the two events occurs

A research was conducted to improve the safety plans in a factory. In this study, the accidental data of the factory for the last 50 weeks were compiled. These data are grouped into the frequency distribution as shown below:

Number of Accidents

Numbers of Weeks

0-5

8

5-10

22

10-15

10

15-20

8

20-25

2

Draw a histogram and calculate the average number of accidents per week.

A cricket ball manufacturing company wants to check the variation in the weight of the balls. For this, 25 samples each of size 4, are selected and the weight of each ball is measured (in grams). The sum of the sample average and the sum of Sample ranges were found to be Σxi25𝑖=1=4010 Grams and Σ𝑅𝑖25𝑖=1=72 grams, respectively. Computer the control limits for the X and R-charts. It is given that A2 = 0.729, D3 = 0 and D4 = 2.282.

How many different ways can 3 bus drivers be selected from 11 bus drivers for a public transport service in a city

For a given discrete non-negative random variable, 𝑝𝑥 = 𝑃(𝑋 = 𝑥). Find 𝑥 such that 𝑝𝑥 > 𝑝𝑥+1, for the following distributions. a. 𝑋 is a binomial distribution with 𝑛 = 16 and 𝑝 = 0.5 b. 𝑋 is a Poisson distribution with 𝜆 = 8 c. 𝑋 is a Negative Binomial with 𝑟 = 5 and 𝑝 = 0.6 State the value of 𝑥 in the above sections. Verify whether the distributions are skewed for each section.

The operations manager of a sales company wants to see whether there is a significant difference in the ages of male and female customers. He selected a sample of 35 samples for each group. The ages are shown in the table below:

A researcher reports that the average salary of College Deans is more than Php 63,000. A sample of 35 College Deans has a mean salary of Php 65,700. At a = 0.01, test the claim that the CollegeDeans earn more than Php 63, 000 a month. The standard deviation of the population is Php 5,250. 

A researcher reports that the average salary of College Deans is more than Php 63,000. A sample of 35 College Deans has a mean salary of Php 65,700. At a = 0.01, test the claim that the CollegeDeans earn more than Php 63, 000 a month. The standard deviation of the population is Php 5,250.