1. (5 points) When a histogram has a longer tail to the left, it is said to be

symmetrical

skewed to the left

skewed to the right

none of the alternatives is correct

2. (5 points) The measure of center which is most likely to be inuenced by extreme values is

Range

Median

Mode

Mea

3. (5 points) Choose the right option:

The mean of the sample is always smaller than the mean of the population from which the sample

was taken.

The mean of the sample can never be zero.

The mean of the sample can never be negative.

None of these alternatives is correct.

4. (5 points) The value which has half of the observations above it and half the observations below it is

called the

Range

Mode

Median

Mean

5.(5 points) Two events are mutually exclusive

if their intersection is one.

if their intersection is zero.

if P(A \ B) = P(A) P(B).

None of the alternatives are corr

6. (5 points) Which of the following statements is true?

For an event A, 1 P(A) 1.

For an event A, P(A) = 1 P(Ac).

For any two events A and B, P(A) + P(B) = 1

For any two events A and B, P(A [ B) = P(A) + P(B)

7. (5 points) Two events with non-zero probabilities

can be both mutually exclusive and independent.

cannot be both mutually exclusive and independent.

are always mutually exclusive.

are always independent.

8. (5 points) If A and B are independent events with P(A) = 0:65 and P(A \ B) = 0:29, then P(B) is

equal to

9. (10 points) Probability that a family has a car, has a bike, has both a car and a bike is equal to 0.61,

0.25, 0.08 respectively. If we randomly choose a family, calculate the following probabilities:

(1) (5 points) Probability that the family does not have a car.

(2) (5 points) Probability that the family has at least one of them.

10. (20 points) A device is set to ll bottle of juice with only 330 grams. The amount of juice that device

pours into bottles has a normal distribution with mean of 330 gram and std of 5. Given this information,

calculate the following probabilities:

(1) (10 points) A random bottle has between 322 and 328 grams of juice.

(2) (10 points) A random bottle has more than 335 grams of juice.

11. (10 points) Age for employees working in a company follow a normal distribution with mean of 35 and

std of 12 years. If the company wanted to retire anybody who is older than 55, what percentage of employees would have to retire?

12. (20 points) Company that produces ne crystal knows from experience that 10% of its goblets have

cosmetic aws and must be classied as second.

(1) (10 points) Among six randomly selected goblets, how likely is it that only one is second?

(2) (10 points) Among six randomly selected goblets, what is the probability that at most two are

second?