10.If there is a very weak correlation between two variables then the correlation coefficient must be

Select one:

a. much smaller than 0, if the correlation is negative

b. much larger than 0, regardless of whether the correlation is negative or positive

c. equal to 1

d. any value larger than 1

e. None of these alternatives is correct

11.Which of the following statements concerning area under Z-distribution is/are true?

I. If a z-score is negative, the area to its right is greater than 0.5.

II. If the area to the right of a z-score is less than 0.5, the z-score is negative.

III. If a z-score is positive, the area to its left is less than 0.5

Select one:

a. I and II only

b. I and III only

c. All of them are true

d. I only

e. II and III only

12.A gas station in a town only sells two types of fuel: regular and diesel. The manager knows from past experience that 90% of all customers purchase regular fuel and 10% purchase diesel. A random sample of 100 customers is selected. What is the approximate probability that less than 80 of them purchase regular fuel?

Select one:

a. 0.0004

b. 0.2

c. 0.8

d. 0.5

e. 0.9996

13.Government officials in Manitoba would like to determine if the average entry level annual income of women working in the tech industry has increased since 2014. Researchers at the University of Manitoba determined that in 2014 the average entry level annual income for women working in a technology related profession (e.g., Artificial Intelligence) was $91,000 with a standard deviation of $1,400. The research team conducted a survey in 2021 where they randomly sampled 51 female working professionals who have been employed in a technology related field for less than 14 months. They determined that the sampled women had a mean annual income of $90,000 with a standard deviation of $2,000. Annual income is known to follow a normal distribution.(don't use excel)

(a)Construct a 92% confidence interval for the true mean annual income in 2021