Question

5. The probability of a person getting the flu this year is 0.15. If we have a group of 20 compute the following. (10 points) a. Standard deviation __1.60______ b. Probability that 2 people have the flu ___0.229_____ c. Probability that less than 4 people have the flu ____0.648____ d. Probability that at least one person has the flu ____0.961____ e. Probability that at least 3 people have the flu ____0.595____ f. A normal distribution of has a mean of 20 and a standard deviation of 10. Find the z-scores corresponding to each of the following values: (10 points) a. What is the z score for a value of 30? ___1_____ b. What is the z score for a value of 10? ___-1_____ c. What is the z score for a value of 15? ____-0.5____ d. What it P(20 10)? ________ f. What is P (x < 15)? ________ g. What is probability that z greater than 25 and less than 20 ________ h. What z value corresponds to a probability of that x < 31 ________ i. What z value corresponds to the 60th percentile? ________ j. If z = 2.5 what x value corresponds to this value. ________

Answer 1

The answers that are given already are correct.

d. P(20 10) is a typing error in the question. It needs to be corrected to be answered.

f. P(X<15) = P(Z<15-20/10) = P(Z<-0.5) = 1- P(Z<0.5) = 1- 0.69146 = 0.30854

g. It. Should be probability that X is not Z since Z lies between -3 to +3. So, P(X>25 and X<20) = P(Z>0.5) + P(Z<0) = 1- P(Z<0.5) + P(Z<0) = 1-0.69146 + 0.5 = 0.80854

h. Z value = 31- 20/10 = 1.1

I. Z value corresponding to the 60th percentile = 0.2533 (from the standard normal distribution table)

j. X- 20/10 = 2.5

So, X= 20+ 2.5*10 = 45