Statistics and Probability Answers

A high-end computer manufacturer sets the retail cost of their computers based on the manufacturing cost. The average manufacturing cost of their computers is reported to be $1800 with a standard deviation of $500. However, the executive of the company suspected that there might be an error in the reporting. The company randomly selects 35 computers from its facilities and finds that the mean cost to produce each computer is $1950.

a) State the appropriate hypotheses to test whether the mean manufacturing cost is the same as the one reported by the manufacturer. [2 marks]

b) Describe Type I and Type II errors in this context, and comment on the severity of each type of error. [3 marks]

c) Test the hypotheses stated in part (a) at a 1% level of significance, and comment on your findings. [5 marks]

The weekly electronics sales of Samsung showrooms is said to follow a normal distribution with an average of 257 thousand taka and a standard deviation of 23 thousand taka. The showrooms that are able to record sales between 245 thousand to 270 thousand taka per week are labelled as “Value Stores”.

a) What is the probability that a randomly selected showroom records sales of more than 254 thousand taka a week? [2 marks]

b) Determine the 48th percentile value of the weekly sales. [2 marks]

c) What is the probability that a randomly selected showroom will not be labelled as a “Value Store”? [2 marks]

d) Clearance sales are often held at showrooms that fall in the bottom 11.35% among the value stores. What is the minimum sales a “Value Store” should record if it is to avoid holding a clearance sale? [4 marks]

The latest M1 Macbook Air and Macbook Pro are available for sale at the Apple Store in Gulshan. 70% of the people who want to buy a new Macbook prefer the Macbook Air, while the rest prefer the Macbook Pro. Suppose 16 customers were randomly selected among those shopping for Macbooks on a specific day.

a) What is the mean value and the standard deviation of the number of people who want to purchase a Macbook Air? [2 marks]

b) What is the probability that the number of people who want a Macbook Air is more than two standard deviations away from the mean value? [4 marks]

c) The Apple Store only has 11 Macbook Airs and 14 Macbook Pros in stock. If the 16 people come in one after another to purchase a Macbook, what is the probability that all 16 will get the type of Macbook they want? [4 marks]

Take a sample of 60 grades and test the following:

1) Test for the hypothesis that the average grade is not 75. 

2) Test for the hypothesis that the average grade below is higher than 75.

3) Calculate the confidence limits for the population mean at 95 %

A fair six-sided dice is thrown and the scores are noted.Event X: The total of the two scores is 4.Even Y: The first score is 2 or 5.

a)Construct the table by showing the sample spaces.

b)Find the probability of Xand Y.

c)Are events X and Y independent?

A population consists of the five measurements 2, 6, 8, 0, and 1 with a sample size 4. Find the variance of the sample means

The average cholesterol content of a 25 canned goods is 215 miligrams,and the standard deviation is 15 miligrams assume that the variable is normally distributed.if sample of 25 canned goods is selected what is the probability that the mean of the sample will be greater than 220 miligrams

Compute the population mean 2,5,7,9,10,11,12

How to find correlation coefficient

 The marks of 500 candidates in an examination are normally distributed 

with mean of 45 marks and a standard deviation of 20 marks. 

a) Given that the pass mark is 41, estimate the number of candidates 

who passed the examination.

b) If 5% of the candidates obtained a distinction by scoring x marks or 

more, estimate the value of x.