8/8/2019 Extra Assign T6

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PPS0015 Intro To Probability and Statistics

Assignment (Topic 6)

1. a) There are five distinct customers entered to TnT Restaurant during an hour of a day. The

waiting time for the ordered foods to be served (to the nearest minutes) of these

customers are 12, 18, 11, 14 and 16.

Prepare a sampling distribution of the sample mean, with sample size of four that can

be selected without replacement from this population.

b) It is known that the waiting time for the ordered foods to be served for allcustomers at TnT Restaurant is normally distributed with mean equals to 13.5 minutes

and variance of 3 minutes2. A random sample of 4 customers is selected. Find the

i. probability that the mean waiting time is between 12 and 16 minutes.

ii. percentage that the mean waiting time is less than 14 minutes or more than 14.5

minutes.

2. The drying time (hours) of Nihon latex paint that painted on all locations is normally

distributed with mean of 4.04 and standard deviation of 0.98. A sample of 20 locations is

randomly selected.

a) Find the mean and the standard deviation of the sampling distribution ofx .

b) What is the proportion of the mean drying time, x , that is less than 4.20?c) What percentage of the mean drying time, x , is in between 3.35 and 4.00?

d) Find the probability that the mean drying time, x , is more than 4.54 or less than 3.70?

3. The weight of all college students in Melaka has a mean of 58 kg and a standard

deviation of 8 kg. A random sample of 100 students is selected.

a) Find the probability that the mean weight is within 3 kg of the population mean.

b) Find the probability that the mean weight is between 57.5 kg and 58.7 kg.

c) Find the percentage of the mean weight that is less than 55.5kg or more than 60.5kg.

d) Construct a 95% confidence interval for the mean weight of all college students in

Melaka if the sample mean is 56kg.

4. A travel magazine wanted to estimate the mean amount of leisure time per week enjoyed by

adults. The research department at the magazine took a sample of 36 adults and obtained

the following data on the weekly leisure time (in hours).

15 12 18 23 11 21 16 13 9 19 26 14

7 8 11 15 23 26 10 8 17 21 12 7

19 21 11 13 21 16 14 9 15 12 10 14

a) What is the point estimate of the mean leisure time per week enjoyed by all adults?

b) Construct a 90% and a 99% confidence interval for the mean leisure time by all adults.

c) Why can the normal distribution be used in part (b)?

5. The thickness of the spearmint gum manufactured by a factory is normally distributed with

an average of 7.5 hundredths of an inch. Recently, there is a buyer complaint to the

manufacturer that the average thickness is not equal to 7.5. Rajesh as the engineer in the

factory is instructed to investigate the thickness. Data below gives the thickness (in

hundredths of an inch) of 25 gums that Rajesh selected randomly from the production line.

7.65 7.60 7.65 7.70 7.55 7.55 7.40 7.40 7.50 7.50 7.60 7.65 7.65

7.55 7.70 7.70 7.70 7.45 7.50 7.50 7.45 7.55 7.70 7.65 7.60

a) Give a point estimate of the mean thickness of all gums produced by this

factory.

b) Construct a 95% and a 98% confidence interval for the mean thickness of all

gums. What interpretation can Rajesh made in order to report to his boss.c) Construct the confidence intervals in part (b) if another sample with size 36 is

collected and this sample produced the same sample mean and sample standard

deviation as the above data.

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8/8/2019 Extra Assign T6

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PPS0015 Intro To Probability and Statistics

d) What can you observe based on the answers in part (b) & (c)?

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