4.Employees in a manufacturing plant worked an average of 62hours of overtimelast year, with a standard deviation of 15hours.

The labor union is engaged in negotiations with the company's HR department over thework rules and overtime policies. Together, they sampled 36 employees at random.

a. What is the probability that the average number of overtime hours worked last year by these 36 employees will be less than 65hours?___________________

b. What is the probability that the 36 employee's average overtime hours will be between 55and 65 hours?_________________________

5. A company producingbags of sugar claims that each bag contains an average of 20.5 ounces. The weights of filled bags follow a normal distribution with a standard deviation of 0.5 ounces.

A consumer advocacy group suspects that the sugar company's claim about its bags of sugar may not be true.The consumer advocacy group has randomly purchased 100 bags of sugar and they intend to file a lawsuit against the sugar company if the sampled bag weights indicate that the company is significantly underfilling the bags.

The group discussed several ways of testing the company's claim. Understanding that some individual bags will weighmore, and some less, than the company's stated average,the group decided that it's more appropriate to look at the mean weight of the sampled bags, rather than individual bags. The group finally decided on the following criteria:

• The consumer advocacy group declared that it will file a lawsuit against the sugar company if the average weight of the sampled 100 bags is less than the 5th percentile of all possible average weights they might see from a sample of 100 bags. That is, if their sample mean bag weight is in the lower 5%.

a. Assuming the company's claims about its bag weights are true, what is the 5th percentile of all possible sample mean bag weights the groupmight see when sampling 100 bags of sugar?__________________ ounces

After defining their cutoff sample mean weight for testing, the advocacy groupsampled n = 100 bags and calculated asample mean bag weight of 20.39 ounces.

b. Using the advocacy group's proposed testing criteria, should the reject the sugar company's claim of an average 20.5 bag weight and file a lawsuit, or should they wait until they have stronger evidence?______________________ (Enter 0 if your answer is "file a lawsuit". Enter 1 if your answer is "wait until they have stronger evidence")

c. Given that the company has stated their bags contain, on average, 20.5 ounces, what is the probability that the consumer group could sample 100 bags and get a samplemean weight of 20.39 ounces or less?______________

Note 1:Final answers that include decimal places should be written out to 3 decimals places,after rounding. For example, if your final answer is 7.1234, then enter 7.123. If your answer is 0.1235, then enter 0.124

Note: Do not use commas. Show all work.

Accepted characters: numbers, decimal point markers, sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation).NOTE:For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form {a + bi} where "a" and "b" need to have explicitly stated values.For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.