Applied Management Statistics – Homework 5 complete solutions correct answers key

Applied Management Statistics – Homework 5 complete solutions correct answers key 

1. (Binomial distribution) Suppose that doctors have observed that 30% of the poeple who

take vitamine C do not catch the flu during the winter. If we take 9 of them, what is the

probability, that all of them have cought the flu? What about only 0, 1 or 2 (together)? And

that exactly 5?

2. Psychologists observed that in city A, the time people spend sleeping follows a normal

distribution. They have measured it for 7 people and found: 5.5, 7.2, 8.2, 6.8, 4.5, 7.4, 6.5.

Estimate the mean and the standard deviation. Determine the 68% and 95% confidence

intervals. Supposing that your estimations are correct, determine the probability that a

randomly chosen person sleeps less than 7 hours normally. What about more than 6? The

probability that it is between 5 and 6.5 hours?

3. (Optional) In city A, the number of cars a person has possessed in his/her life follows a

Poisson distribution with parameter 7. Choosing randomly somebody, what is the

probability that he/she has had 3 cars? 10 cars? 4, 5 or 6 cars?

4. Assume that amount of water we drink a day is of normal distribution and with mean 2 and

standard deviation of 0.4. Determine the confidence intervals (68% and 95%), and the

probabilities of (having randomly chosen somebody) finding that the person drinks less than

2.2 litres/day, less than 1.6 litres, more than 3 litres? Between 1.8 and 2.8 litres?

5. (Binomial distribution) Having seen that when we pronounce a word, 99% of the ones

present understand it, having 100 people listening, what is the probability that everybody

has understood it? What is the probability that 85 has understood it?

6. We have three groups of students: A, B and C, with all of them having 5 students. If we

choose randomly 3 students, what is the probability that all of them belong to the same

group? What is the probability that each of them belongs to different groups?

7. We have a list of 21 people, 12 of them are friends (5 men and 7 women) and 9 of them are

from the family (6 men and 3 women). If we randomly choose 3 people, what is the

probability that all of them are men or from the family?

8. We have measured the weight of the bread made in a bakery and have found the following

(in grams): 1030, 1020, 1000, 970, 980, 1010, 1020, 990, 1010, 1020. Calculate the mean

and the standard deviation. Suppose that is of normal distribution. Determine the 68% and

95% confidence interval. If we randomly choose a bread, what is the probability that its

weight is less than 970g? More than 1005? between 980 and 1020?

9. In Country Z, you can play the lottery choosing 5 numbers out of 20. If your ticket matches

5 numbers, the prize is 1200€, if it mathes 4, it is 500€, and 100€, 27€ and 5€ in case of 3,

2 and 1 matches. Would you play it for 20€? (Is the expected value greater than 20€?)

What about 15€ or 25€?

Binomial distribution: We have n experiments. The probability that one is successful is p. Then, let

X be the probability that k experiments have been successful. It is given by: P(X=k)=nCk pk (1–p)n-k.