Galway Bay Restaurants (GBR) has several restaurants around the country Since the outbreak of COVID-19 and subsequent reduction in the restaurant business, the owners of GBR are seeking to reduce wages in a bid to make some cost savings and avoid job loss. To help them inform the decision the owners of GBR would like to gain information on the amount of tip a waiter/waitress can expect to earn per bill. Analysis of 500 recent bills indicated that the waiter/waitress earned the following amounts in tips per 8-hour shift.

i. What is the probability of a tip of £200 or more?

ii. Are the categories €0 up to €20, €20 up to €50, and so on considered mutually exclusive?

iii. What is the probability of a tip of up to €50? iv. What is the probability of a tip of less than €200?

The monthly expenditure by households on electricity bills follows a normal probability distribution with a mean of €50 and a standard deviation of €4. On the basis of this information:

i. What is the probability of selecting a household whose bill is between €44 and €55?

ii. What is the probability of selecting a household whose bill is greater than €55?

iii. Compute the probability of a value between €52 and €55.

The amount of water in a 12-ounce bottle is uniformly distributed between 11.96 ounces and 12.05 ounces

i. What is the mean amount per bottle

ii. What is the standard deviation amount per bottle?

iii. What is the probability of selecting a bottle of water and finding it has less than 12 ounces?

iv. What is the probability of selecting a bottle of water and finding it has more than 11.98 ounces?

The quality control department in a local medical device company employs five quality assurance technicians during the day shift. Listed below is the number of times each technician instructed the production team to shut down manufacturing last week

i. How many different samples of two technicians are possible from this population

ii. List all possible samples of two observations each and compute the mean of each sample

iii. Compare the mean of the sample means with the population mean

v. Compare the shape of the population distribution with the shape of the distribution of the sample means

A recent study revealed that a typical NUIG student coffee drinkers consume an average of 3.1 cups per day. A sample of 12 lecturers revealed that they consumed the following amounts of coffee, reported in cups, yesterday.

3.1 3.3 3.5 2.6 2.6 4.3 4.4 3.8 3.1 4.1 3.1 3.2

At the 0.05 significance level, do theses sample data suggest there is a difference between student coffee drinkers sand the sample mean from the lecturers?

Given the following hypothesis

A random sample of six students resulted in the following values for annual lecture attendance: 118,105,112,119,105 and 111. Assume a normal population. Using the 0.05 significance level can we conclude that the mean is different from 100?

i. State the decision rule

ii. Compute the value of the t statistic

iii. What is your decision regarding the null hypothesis?

iv. Estimate the p-value