Mean and Standard Deviation of the Sample Data - Mathematics Assignment Help

Assignment Task :

M1 has a small business selling recycled origami paper. Nina bought some of this paper and is complaining that the paper is not square and wants a refund. Nina claims to have measured all the sides of the first 3 pieces of paper from the pack of paper she bought from MJ.

The side length data (in millimetres) that Nina provided in an email are: {150.3, 152, 155.5, 148.0, 160.65, 156.01, 165.0, 153, 149.2, 152.3, 157.87, 151.99, 185)

a) Determine the mean and standard deviation of the sample data.

b) Determine the 5-number summary.

c) Identify any outliers

d) Construct a box plot

e) Determine the 99% confidence interval for the above data assuming that the population is normally distributed.

f) MJ does NOT want to refund the $2.37 that Nina paid for the recycled origami paper.

Use your knowledge of statistics, the information provided and/or calculated to advise MJ on what she could say to reject Nina's claim. 
 

2. A thick shake dispenser at a Curtin food van is designed so that the amount dispensed per large thick shake is 650 ml with a standard deviation of 11 mi. Repeated testing has confirmed that the distribution is normal.

a) What is the probability a large thick shake contains:

i) Less than 650 ml?

ii) Exactly 670 ml?

iii) Between 645 ml and 652 ml?

iv) Above what amount (to the neatest nil) does the top 7% of the distribution lie?

b) A sample of 9 large thick shakes was taken:

i) Determine the probability that the sample means lies between 645 ml and 652 ml.

ii) Explain why this probability is different to the answer in a 

iii; other than the formula being different. 
 

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