Reference no: EM13582960
Q1. The monthly utility bills are normally distributed with a mean value of $130 and a standard deviation of $15.
(a) Find the probability of having a utility bill between 100 and 150.
(b) Find the probability of having a utility bill less than $90.
(c) Find the probability of having a utility bill more than $160.
Q2. A Mall manager claims that in average every customer spends $37 per a single visit to the mall. To test this claim, you took a sample of 64 customers and found the sample mean to be $34 and the sample standard deviation to be $5. At alpha = 0.05, test the Mall's manager claim. Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results.
Q3. A bank manager wanted to estimate the mean number of transactions businesses make per month. For a sample of 60 businesses, he found the mean number of transaction per month to be 38 and the standard deviation to be 8.5 transactions.
(a) Find a 95% confidence interval for the mean number of business transactions per month. Show your calculations and/or explain the process used to obtain the interval.
(b) Interpret this confidence interval and write a sentence that explains it.
Q4. A company's CEO wanted to estimate the percentage of defective product per shipment. In a sample containing 600 products, he found 45 defective products.
(a) Find a 99% confidence interval for the true proportion of defective product. Show your calculations and/or explain the process used to obtain the interval.
(b) Interpret this confidence interval and write a sentence that explains it.
Q5. The ages of 10 students are listed in years:{ 17,22,19,24,21,23,29,18,22,28 }
(a) Find the mean, median, mode, sample variance, and range.
(b) Do you think that this sample might have come from a normal population? Why or why not?