# EBook Problems Distrib MeanVar

## EBook Problems Set - Expectation (Mean) and Variance

### Problem 1

Ming’s Seafood Shop stocks live lobsters. Ming pays $6.00 for each lobster and sells each one for$12.00. The demand X for these lobsters in a given day has the following probability mass function.

 X 0 1 2 3 4 5 P(x) 0.05 0.15 0.3 0.2 0.2 0.1

What is the Expected Demand?

(a) 13.5
(b) 3.1
(c) 2.65
(d) 5.2

### Problem 2

If sampling distributions of sample means are examined for samples of size 1, 5, 10, 16 and 50, you will notice that as sample size increases, the shape of the sampling distribution appears more like that of the:

(a) normal distribution
(b) uniform distribution
(c) population distribution
(d) binomial distribution

### Problem 3

The number of flaws on an electroplated automobile grill is known to have following probability distribution:

 X 0 1 2 3 P(X) 0.8 0.1 0.05 0.05

For a random sample of 200 grills, calculate the approximate probability that the average number of flaws per grill exceeds 0.4

(a) 0.0002
(b) None of the above
(c) 1
(d) 0.1860 approximately

### Problem 4

The number of flaws on an electroplated automobile grill is known to have following probability distribution:

 X 0 1 2 3 P(X) 0.8 0.1 0.05 0.05

What would be the standard deviation of the sample means if we took 100 samples, each sample with 200 grills, and computed their sample means?

(a) None of the above
(b) 0.89269
(c) 0.0560
(d) 0.6275

### Problem 5

Defective Tires The probability distribution of x, the number of defective tires on randomly selected automobiles at a certain inspection station, is given in the accompanying table:

 X = defective 0 1 2 3 4 Probability (X) 0.54 0.16 0.06 0.04 0.2

After you calculate the expected number (the mean) of defective tires, determine the probability that x exceeds the expected value.

(a) None of these values
(b) 0.54
(c) 0.16
(d) 0.30
(e) 0.70

### Problem 6

Suppose that there were two sections of Statistics 12 last quarter. The morning section had 100 students and their average on the final was 82. The afternoon section of 60 students had an average of 74 on the same final. What is the average on the final if we combine the scores for both classes?

(a) 78
(b) 76
(c) The average cannot be calculated since individual scores are not available
(d) 79
(e) 80