Question

In a large Insurance Company in U.S., people over age thirty five have an annual income that follows a normal distribution with mean 70,000 and standard deviation 9,000. The incomes of those under age thirty five are also approximately normal, but with mean 45,000 and standard deviation 8,000. With the above information simulate 10000 employees over 35 and 10000 employees under 35 and answer the questions. 21. What is the approximate probability that a randomly picked, employee over 35 will have an income lower than or equal to 60,000? Pick the closest answer. (4 points) a. About 15% O b. About 25% C. About 35% : d. About 55% 22. what would be a range [A to B] for the income, which would contain 95% of the employee under 35? Pick the closest answer. (4 points) a. Between 35,000 and 65,000 b. Between 29,000 and 61,000 c. Between 52,000 and 88,000 d. Between 35,000 and 60,000 сь

Answer 1

(1) mean = 70000

Standard deviation = 9000

Z score for 60000 = 60000 - 70000/9000 = - 10000/9000 = -1.11

Area under z score - 1.11 = 0.1335 ~ 15%

Option (a) 15%

(2) mean = 45000

Standard deviation = 8000

by seeing the z score table we can say that for 95% the z score should be = 1.65

Now, let the salary be x

As we know the z score so

X - 45000/8000 = 1.65

=> x - 45000 = 1.65 × 8000

=> x - 45000 = 13200

=> x = 58000

And we will take it as + 13200

So the range of the salary will be 31800 to 58200

Option (b) is correct 29000 to 61000

(3) mean = 45000

Standard deviation = 8000

Z score for 50000 = 50000 - 45000/8000 = 5000/8000 = 0.625

Area under z score 0.625 = 0.7324

As it is asked more than 50000, so we will subtract it from 1

= 1 - 0.73

= 27

Option (c) is correct about 27%

(4) mean = 45000

Standard deviation = 8000

Z score for 35000 = 35000 - 45000/8000 = - 10000/8000 = -1.25

Area under z score - 1.25 = 0.1056

Z score for 50000 = 50000 - 45000/8000 = 5000/8000 = 0.625

Area under z score 0.625 = 0.7324

So difference between is = 0.7324 - 0.1056 ~ 63%

Option (c) is correct about 65%

Note:- only 4 questions are allowed to answer as per HOMEWORKLIB RULES if a list of questions are asked