Next TWO questions are based on the following: Tom is a salesman. He receives 20

Question

Next TWO questions are based on the following: Tom is a salesman. He receives 20% of the price of the item sold as sales commission plus a fixed salary of $200 per week. Tom's average weekly sales is 25 items with a standard deviation of 8. The average price of items Tom sells is $250. Bob works 46 weeks a year. 15 Tom's average annual earnings is ________. a $66,700 b $64,800 c $62,600 d $60,500 16 In the previous question, what is the standard deviation of the annual salary? a $20,360 b $18,400 c $16,600 d $14,750 Next SIX questions are based on the following: Consider a binomial experiment with n = 10 and = 0.35. Let x denote the number of successes. 17 f(x = 5) = _______. a 0.1272 b 0.1536 c 0.0823 d 0.0595 18 f(x 3) = _______ f(x 3) = _______ a 0.2616 0.4862 b 0.2616 0.5138 c 0.5138 0.7384 d 0.5138 0.4862 19 E(x) = ______. a 4.5 b 4 c 3.5 d 3 20 var(x) = ______. a 3.775 b 3.275 c 2.775 d 2.275 21 Suppose you are receiving a large shipment of Gizmos. The manufacturing standards provide that 1% of Gizmos turn out defective. You randomly select a sample of n = 20 from each lot and return the shipment if more than 1 are found defective. The probability of returning a shipment is: a 0.0169 b 0.0116 c 0.0058 d 0.0025 22 A test has 50 multiple choice questions. Each question has five choices. The test scores are measured from a scale of 100. If a student guesses the answers for all 50 questions, what is the expected score? a 30 b 25 c 20 d 15 Next TWO questions are based on the following: Tom is a salesman. He receives 20% of the price of the item sold as sales commission plus a fixed salary of $200 per week. Tom's average weekly sales is 25 items with a standard deviation of 8. The average price of items Tom sells is $250. Bob works 46 weeks a year. 15 Tom's average annual earnings is ________. a $66,700 b $64,800 c $62,600 d $60,500 16 In the previous question, what is the standard deviation of the annual salary? a $20,360 b $18,400 c $16,600 d $14,750 Next SIX questions are based on the following: Consider a binomial experiment with n = 10 and = 0.35. Let x denote the number of successes. 17 f(x = 5) = _______. a 0.1272 b 0.1536 c 0.0823 d 0.0595 18 f(x 3) = _______ f(x 3) = _______ a 0.2616 0.4862 b 0.2616 0.5138 c 0.5138 0.7384 d 0.5138 0.4862 19 E(x) = ______. a 4.5 b 4 c 3.5 d 3 20 var(x) = ______. a 3.775 b 3.275 c 2.775 d 2.275 21 Suppose you are receiving a large shipment of Gizmos. The manufacturing standards provide that 1% of Gizmos turn out defective. You randomly select a sample of n = 20 from each lot and return the shipment if more than 1 are found defective. The probability of returning a shipment is: a 0.0169 b 0.0116 c 0.0058 d 0.0025 22 A test has 50 multiple choice questions. Each question has five choices. The test scores are measured from a scale of 100. If a student guesses the answers for all 50 questions, what is the expected score? a 30 b 25 c 20 d 15

Explanation / Answer

15) Let x = weekly sales.

E(x) =25

Let y = weekly earnings.

y = a + bx

a =$200

Commission: percent of sales price =0.2

Average sales price =$250

b = 0.2 × 250 =$50

E(y) = 200 + 50E(x) = $1,450

Let z = annual earnings

z = 46yE(z) = 46E(y)E(z) =$66,700

Option-A) $66,700

16) sd(x) =8

sd(y) = bsd(x) =$400

sd(z) = 46sd(y) =$18,400

Option-B) $18,400

17) n = 10

p = 0.35

f(X = x) = 10Cx * 0.35x * (1 - 0.35)10-x

f(X = 5) = 10C5 * 0.355 * 0.655 = 0.1536

Option-B) 0.1536

18) f(X < 3) = f(X = 0) + f(X = 1) + f(X = 2) + f(X = 3)

= 10C0 * 0.350 * 0.6510 + 10C1 * 0.351 * 0.659 + 10C2 * 0.352 * 0.658 + 10C3 * 0.353 * 0.657

= 0.5138

f(X > 3) = 1 - [f(X = 0) + f(X = 1) + f(X = 2) ]

= 1 - [10C0 * 0.350 * 0.6510 + 10C1 * 0.351 * 0.659 + 10C2 * 0.352 * 0.658 ]

= 1 - 0.2616

= 0.7384

Option-C) 0.7384

19) E(X) = n * p = 10 * 0.35 = 3.5

Option-C) 3.5

20) Var(X) = n * p * (1 - p) = 10 * 0.35 * 0.65 = 2.275

Option-D) 2.275

21) p = 0.01

n = 20

P(X > 1) = 1 - [P(X = 0) + P(X = 1)]

= 1 - [20C0 * 0.010 * 0.9920 + 20C1 * 0.011 * 0.9919]

= 1 - 0.9831

= 0.0169

Option-A) 0.0169

22) P(guessing correct choice) = 1/5 = 0.2

n = 50

Expected number of questions to be corrected = 50 * 0.2 = 10

Expected score = 10 * 2 = 20

Option-C) 20

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