1. A company surveyed their clients on how much they were willing to pay for their new product, model X. 80 clients returned the survey. The average amount they were willing to pay for Model X was $840. The standard deviation is $ 230. What is the 95% confidence interval for the mean value clients are willing to pay for model X?
2. Income tax returns in Canada in 2018 averaged $1432 in refunds for taxpayers with the standard deviation of $725. The amounts owed or due on tax returns are normally distributed.

a. What proportion of the tax returns shows a refund of more than $1600?

b. What proportion of the tax returns shows a refund between $700 and $1300?

c. What amount of the tax refund should a person receive to be in the top 5% of the distribution?

3.a.To conduct a research project on college student income, the number of students to sample needs to be calculated. To estimate the mean population income, we decide to use a 99% level of confidence. The desired margin of error is plus or minus $150. The standard deviation from other studies of student income is $1500. What sample size should be used?

b. College X is concerned about their employees making use of their email for non-business purposes. You have been approached to assist in this matter. College X decides on a 95% confidence level and state that the estimation proportion must be within 3 percent of the population proportion. A pilot survey reveals that 12 out of 50 emails sampled were not for business purposes. How many emails should be surveyed to meet your requirements?

4.Lety= number of cars a person owns. According to Statistics Canada, for residents of Canadayhas probability distribution P (0) = 0.16 P = (1) 0.70 and P (2) = 0.14, with negligible probability for higher values ofy.

a. Construct a table showing the probability distribution ofy.

b. Find the probability that a Canadian owns 1 car or less (none).

c. Find the mean of this probability distribution.