Statistics and Probability Answers

One of the psychological tests conducted by the guidance counselors in a public school is the Survey of Study Habits and Attitudes (SSHA) that measures student’s attitudes toward studying. The mean score of Senior High students is with standard deviation of . Mrs. Suacillo suspects that older students have better attitudes toward school. He randomly selects Grade students who are at least years old and gives them SSHA. The test result has a mean score of points. Is there a reason to believe that the claim of the guidance counselors is correct? Assume that the population mean score is normally distributed. Carry out a significance test at level. \

The daily net profit for spaza shop follows a normal distribution with a mean of R220 and a standard deviation of R175.

a) The probability that the daily net profit exceeds R250 is (answer to 2 decimal places)   

b) The cut-off value for lowest 40 % of daily net profits is (in Rands and cents) 

The monthly amount spent on stationery in a large company has a normal distribution with mean R2500 and standard deviation R150. How much should the company budget for stationery if the chance of exceeding the budget has to be only 2.5%?

A pizza parlour will deliver a pizza take-away order to the customer if s/he lives within a 5 kilometre radius from the pizza parlour. If the customer lives within this radius, it is found that the time taken to receive the pizza is normally distributed with a mean time of 45 minutes and a standard deviation of 8 minutes. Paul has relocated and now lives within the 5 kilometre radius. He orders a pizza from the pizza parlour. The probability that it takes between 43 and 49 minutes for him to receive his pizza is (correct to 2 decimal places)

A pizza parlour will deliver a pizza take-away order to the customer if s/he lives within a 5 kilometre radius from the pizza parlour. If the customer lives within this radius, it is found that the time taken to receive the pizza is normally distributed with a mean time of 45 minutes and a standard deviation of 8 minutes. If the time to receiving the pizza exceeds a particular time period, the customer gets the pizza free of charge. What should the approximate time limit (to the nearest minute) until delivery for the pizza be if the pizza parlour wants no more than 10% of the customers to get a free pizza?

Identify the lower and upper confidence limits of 32.75 < population mean < 37.77

A population consists of value (2,3,5). Consider all possible samples of size n=2 that can be drawn with resplacement from this population

A government agency is investigating a complaint from some concerned citizens who said that there is short-weight selling of rice in a certain town. An agent manufacturer took a random sample of 20 sacks of "50 kilo" sacks of rice from a large shipment and finda that the mean weight is 49.7 kilogram with the standard deviation of 0.35 kilogram. The level of significance is 0.01