Question

Sampling, Confidence Intervals, Sample Sizes

SKETCH Required. PLACE ANSWER WITH PROBABILITY NOTATION IN RECTANGE.

3) A professor has given the same multiple choice final exam in his Economics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a population standard deviation of 12. The professor offers his class of 36 a pizza party if the class average is above 80. What is the probability that he will have to deliver on his promise?

4. The labor force participation rate was 63.7%. A marketing company asks 120 working-age people if they either have a job or are looking for a job. What is the probability that less than 60% of those surveyed are members of the labor force?

Answer 1

Solution 3:

Given that mean, = 76, standard deviation, = 12 and sample size, = 36

The professor will deliver his promise when the class average is above 80 i.e. X > 80. We have to find P (> 80)

The respective Z- score with = 80 is

2

Now, we use Z-tables to find the probability of Z greater than 2

P (Z > 2) = 1 - P (Z 2)

= 1 - 0.9772

= 0.0228

Hence, the probability that he will have to deliver on his promise is 0.0228