Question

Please answer all with steps shown. You will be rated.

Two plants, A and B, ship appliances to a warehouse.  Plant A produces 60% of the warehouse's inventory and plant B produces the rest of the warehouse's inventory. It is known that 2% of the appliances from plant A are defective and 3% of the appliances from plant B are defective.

a)  (5 points) A warehouse inspector randomly selects an appliance. What is the probability that the appliance is from plant B and not defective?

b)   (5 points) What is the probability that a randomly selected appliance is not defective?

c)  (5 points) Suppose an appliance is not defective. What is the probability that it came from plant A?

The following data is exa score and hours looking at social media in that week of the exa from a sample of 10 students.

Student	1	2	3	4	5	6	7	8	9	10
Exa Score	50	67	72	73	79	83	85	86	89	92
Hours	9.5	9.5	8.2	7.8	6.7	5.9	5.5	4.2	1.8	0.1

a)  (3 points) Using the IQR rule, are there any outliers for the exa scores? If so write down the number(s).  Give the interval that defines the outliers.

b)  (4 points) Determine the correlation coefficient, r, between exa score and hours studied. Interpret what this number means.

c)  (3 points) Determine the least-square regression equation to predict exa scores based on hours studied.  

d)  (3 points) If a student studies for 5 hours what is the predicted exa score?

e) (3 points) Give the residual for student 2.

f)  (4 points) Give the coefficient of determination, , for this least-squares equation. Give the interpretation of this number.

Suppose a local restaurant has only four meals on the menu costing $4, $5, $8, and $10 . The probability distribution (pmf) is below, where X = cost of the meals.  

X	4	5	8	10
f(x) = P(X = x)	0.1	0.3	0.5	0.1

a)  (2 points)  Suppose a random customer orders a meal at this restaurant. What is the probability that the customer's meal will cost at least $8?

b)  (5 points) Find the expected value of the cost of the meal for a random customer.

c)  (5 points) Find the standard deviation of the cost of the meal for a random customer.

d)  (3 points) If the restaurant decided to add $5 more to each meal, what is the expected cost and standard deviation with the $5 added?

Answer 1

1)

P(   Plant A   ) =    0.6
P(   Plant B   ) =    0.4

P(   not defective   | Plant A)=   0.98
P(   not defective   | Plant B)=   0.97

a) P(plant B and not defective) = 0.4*(1-0.03)=0.388

b)

P(not defective) = P(Plant A) * P(not defective| Plant A) + P(Plant B) *P(not defective| Plant B) + P( )*P(not defective| ) =                                    0.6*0.98+0.4*0.97+*=               0.976

c) P(Plant A| not defective) = P(Plant A)*P(not defective| Plant A)/P(not defective)=               0.6*0.98/0.976=       0.6025

c)