TSTA101 Statistics Assessment :

Assignment

Unit: **TSTA101 Introductory Statistics**

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

#### Instructions:

- This is a group assignment. Each student should find your group member by yourself, each group should have no more than 3 students.
- Each group
**MUST**submit one copy of the assignment with a cover sheet; the group member**MUST**sign at the cover sheet. - 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

- Lasts between 5 and 10 minutes
- 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.

- Find the probability that one selected subcomponent is longer than 120cm.
- 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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