Question

Please provide solutions below

1. Suppose College male students’ heights are normally distributed with a mean of µ = 69.5 inches and a standard deviation of σ =2.8 inches.

1. What is the probability that randomly selected male is at least 70.5 inches tall?

[2 marks]

2. If one male student is randomly selected, find the probability that his height is less than 65.2 inches or greater than 71.2 inches.

[3 marks]

3. How tall is Shivam if only 30.5% of students are taller than him (2 decimal places)?

[3 marks]

4. There are 30.5% of all students between Mike’s height and 75 inches. How tall is Mike?

(2 decimal places)

[3 marks]

5. If 25 male students are randomly selected, find the probability that they have a mean height no higher than 70.2 inches.

[3 marks]

2. In a survey conducted to determine, among other things, the cost of vacations, 64 individuals were randomly sampled. Each person was asked to compute the cost of her or his most recent vacation. The sample showed a sample mean of $1810. Assuming that the population standard deviation σ is $600, construct a 90% confidence interval for the average cost of all vacations by filling in the following blanks. (Round confidence limits answer to 2 decimal places).

Critical value =

Point Estimate =

Standard Error of the Estimate =

Margin of Error =

Lower Confidence Limit =

Upper Confidence Limit =

3. The operations manager of a large production plant would like to estimate the average amount of time workers take to assemble a new electronic component. After observing a number of workers assembling similar devices, she estimates that the standard deviation is 0.25 hours. How large a sample of workers should she select if she wishes to estimate the mean assembly time to within 3.2 minutes at the 98% confidence level?

                                       

                                                

4. In a crash test of 26 minivans of a Japanese manufacturer, collision repair costs are found to have a distribution that is roughly bell shaped, with a mean of $1850 and a standard deviation of $340. Construct a 95% confidence interval for the mean repair cost in all such vehicle collisions by filling in the following blanks (Round confidence limits to the nearest dollar).

df =

Critical value =

Point Estimate =

Standard Error of the Estimate =

Margin of Error =

Lower Confidence Limit =

Upper Confidence Limit =

5. A certain factory consumes on average 1000 litres of water per day with a variance (σ²) of 625 litres². A random sample of 100 days taken revealed a mean daily consumption of x = 1006 litres. At α = 0.01, test if the mean daily water intake remains 1000 litres against the alternative that the mean water consumption has changed.

Hypotheses:

Rejection Region:

Test Statistic:

Decision/Conclusion:

6. A car dealership claims that its average service time is less than 7 hours on weekdays. A random sample of 16 service times was recorded and yielded the statistics x=6.75 hours and s= 1.62 hours. Assume service times are normally distributed, is there enough evidence to support the dealership’s claim at 5% significance level?

Hypotheses:

Rejection Region:

Test Statistic:

Decision/Conclusion:

Multiple Choice: Choose the best answer (1 mark each)

1. Scores on an IQ test for the 18-to-30 age group are approximately normally distributed with a mean of 110 and a standard deviation 25. Scores for the 31-to-40 age group are approximately normally distributed with mean 100 and standard deviation 20. Phoebe, who is 25, scores 130 on the test. Amandeep, who is 36, also takes the test and scores 116.

Who scored higher relative to her age group, Phoebe or Amandeep?

1. Phoebe
2. Amandeep
3. They scored the same
4. It cannot be determined with the information given

2. A 99% confidence interval for a population mean is determined to have lower and upper limits of 32.7 and 42.8 respectively. If the confidence level is changed to 95%, then the sample mean

1. becomes smaller
2. becomes larger
3. does not change
4. changes based on the z critical value
5. cannot tell based on the given information

3. The 90% confidence interval estimate for a population mean was 72.49 to 75.78. If the population variance was 324, then the sample size used was:

1. 36
2. 49
3. 64
4. 81
5. None of the above

4. Suppose we wish to test H₀: µ ≥ 20 vs. H₁: µ < 20. What will result if we conclude that the mean is less than 20 when the actual mean is 23?

1. We have made a Type I error.
2. We have made a Type II error.
3. We have made a Type III error.
4. We have made both a Type I error and a Type II error.
5. We have made the correct decision.

Answer 1