\fFor questions 8 through 10, consider a normal distribution X ~ N(1.22,100) Q8 What is the probability that x is less than 1.22? a. 0.1253 b. 0.3495 c. 0.5000 d. 0.5849 Q9 What value of x represents the 90th %-tile? a. 14.02 b. 1.28 c. 5.68 d. 9.45 Q10 What value of x has 80% of other x values larger than it? a. -0.84 b. 0.80 C. 3.86 d. -7.18For questions 11 through 13, suppose the average sale per customer in the deli section of a supermarket is $8.50 with a standard deviation of $2.50. Q11 If 36 customers make purchases on a given day, what are the mean and variance of the mean sale price? a. 8.5, 0.417 b. 8.5, 0.174 c. 8.5, 0.069 d. 0.236, 0.417 Q12 What is the probability that the mean sale price is less than $8 (use n=36 from Q11)? a. 0.1151 b. 0.3936 c. 0.3572 d. 0.6064Q13 Which value of the mean sale price is at the 32"" -tile {use n=36 from (111]? a. 3.?5 h. I192 c. 1&6? d. 3.33 For question 14 and 15, suppose it is well known that 78% of Americans say recycling is the best way to help the environment. Q14 If we randomly survey 100 people, what are the mean and variance of the distribution of the sample proportion that say recycling is the best way to help the environment? a. 0.78, 0.00172 b. 0.78, 0.00563 c. 0.88, 0.00934 d. 0.78, 0.04150 Q15 What is the probability that more than 80 people in the survey say that recycling is the best way to help the environment (use n=100 from Q14)? a. 0.8455 b. 0.6844 c. 0.3156 d. 0.1452Stat 330 Homework #5 For questions 1 through 4, consider a standard normal distribution Z ~ N(0,1) Q1 What is the probability that z is less than 1.45? a. 0.5483 b. 0.9265 C. 0.3356 d. 0.8743 Q2 What is the probability that z is greater than -0.27? a. 0.9438 b. 0.3936 c. 0.3572 d. 0.6064 Q3 What is the probability that z is between -1.22 and 2.34? a. 0.9904 b. 0.1112 C. 0.8792 d. 0.5637Q4 What z value is at the 56th %-tile a. 0.15 b. 1.56 C. -2.33 d. 1.96 For questions 5 through 7, consider a normal distribution X ~ N(5,16) Q5 What is the probability that x is less than 6? a. 0.8455 b. 0.5987 c. 0.2323 d. 0.9453 Q6 What is the probability that x is greater than -1? a. 0.0668 b. 0.4987 c. 0.9332 d. 0.1267