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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