1. a. Find the z value to the left of mean so that 0.025 percentof the area under the distribution curve lies to the left of it.Also report the area that was left over after the lastcalculation.

b. Find area between Z= 0 and Z=1.31

           c.Find probability of P( -1.96≤ z ≤ 1.96) and P (Z=0)                 

1. The average score of a Business Studies graduate is 72 and thestandard deviation is 5. The top 2 percent of the graduates receivea certificate of distinction and the next 5 percent are given achance to apply to the business incubation center for anentrepreneurial venture.

1. What score/marks must you exceed to get a distinction and whatrange of marks is required for the entrepreneurialopportunity.
2. What average must you get in order to avoidfailing.                  

1. The tax rates for basic necessities to be used during theCOVID-19 by households items in cents is as follows:

112	120	98	55	71	35	99	124	64
150	150	55	100	132	20	70	93

1. Find the 99% and 95% confidence interval for the food tax onthe selected items.
2. Which interval is larger and why?
3. If you wanted to convey the true picture of the majority of thepeople to the government which confidence interval would youreport? Give a logicalexplanation.