TSTA101 Statistics Assessment

TSTA101 Statistics Assessment :

Assignment

Unit: TSTA101 Introductory Statistics

Due Date: Monday, 10/10/2022 Total Marks: 25 marks

Instructions:

1. This is a group assignment. Each student should find your group member by yourself, each group should have no more than 3 students.
2. Each group MUST submit one copy of the assignment with a cover sheet; the group member MUST sign at the cover sheet.
3. The assignment MUST submit via tern-it-in before the due day.

Find the following probabilities by checking the z table i)   P (Z>-1.23)

ii)    P(-1.51<Z<1.23)

iii) Z0.045

Part b)                                                                                                 (3 marks)

The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes. Find the probability that a call

1. Lasts between 5 and 10 minutes
2. Lasts more than 7 minutes

Question 2 [6 marks]

Part a)                                                                                                  (3 marks)

A sample of n=16 observations is drawn from a normal population with µ=1000 and σ=200. Find the following.

i)       P( X >1050)

ii)      P(960< X <1050)

Part b)                                                                                                 (3 marks)

An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean=117cm and standard deviation =5.2 cm.

1. Find the probability that one selected subcomponent is longer than 120cm.
2. Find the probability that if four subcomponents are randomly selected, their mean length exceeds 120cm.

Question 3 [6 marks]

Part a)                                                                                                  (3 marks)

The mean of a sample of 25 was calculated as mean of 500. The sample was randomly drawn from a population whose standard deviation is 15. Estimate the population mean with 95% confidence.

Part b)                                                                                                 (3 marks)

The following sample of 16 measurements was selected from a population that is approximately normally distributed.

Construct a 90% confidence interval for the population mean.

Calculate the statistic, set up the rejection region, draw the sampling distribution and interpret the result,

H0:       µ=10

H1:       µ≠10

Given that: σ=10, n=100, X =10, α=0.05.

Part b)                                                                                                 (4 marks)

A business student claims that, on average, an MBA student is required to prepare more than five cases per week. To examine the claim a professor asks a random sample 10 MBA student to report the number of cases they prepare weekly; the professor calculates the mean value and standard deviation, which is 6 and 1.5, respectively. Can the professor conclude at the 5% significance level that the claim is true, assuming that the number of case is normal distribution?

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