Question

1. Assume that every time Jordan plays golf her score is normally distributed with mean 100 and standard deviation 6.
   1. Jordan is playing golf with her friend Joey who gets a score of 112. What is the probability that Jordan gets a score less than or equal to Joey's?
   2. Jordan is playing golf with another friend, Lillian, who gets a score of 106. What is the probability that Jordan gets a score greater than or equal to Lillian's?
   3. For what number is there an 84% probability that Jordan will get a score less than or equal to it? HINT: For instance, 100 is the number that Jordan has a 50% probability of scoring less than or equal to.
   4. These three friends decide to play four games of golf and record their average (mean) scores. Joey's average score is 94 and Lillian’s average score is 103. What is the probability that Jordan’s average score after playing four games of golf is between her two friends’ average scores (greater than or equal to Joey’s and less than or equal to Lillian’s)?

Answer 1

P(z<Z) table :

part 1 :

p(score <= 112) = 0.9772

part 2:

p(score >= 106) = 0.1587

part 3:

p(z<Z) = 0.84

from table z = 1

score = mean + 1*SD = 100+6 = 106

P(score <= 106) = 84%

For score 106 number is there an 84% probability that Jordan will get a score less than or equal to it

part 4:

SDsample = SD/(n^0.5) = SD/(4^0.5) = 6/2 = 3

p(94 <= mean score <= 103) = 0.8186

(please UPVOTE)