Question

2. Chilicheese Games scores arç normally distributed with a mean of 1288 and a standard deviation of (sum of your Mother's and Father's ages). a) Draw a sketch of and label a graph that shows all the information relevant to the problem, including the answer to (b). b) Find the probability that a randomly selected person will have Chilicheese Games score above 1250. Draw a sketch of the distribution and shade in the probability. Also, write out the command you enter in the calculator. c) Find ChiliCheese Games scores of someone who scores below exactly 37.5% of the population. Draw a sketch of the information given. Write out the calculator command you enter. d) An exit interview of 200 people is taken as players leave Chilicheese. Find the probability that the sample mean is less than 1225. Draw a picture of the distribution and shade the probability. Write out the calculator commands you enter. о е прео уре V . N MMI

Answer 1

assuming sum of mother and father's age is 80

hence sd = 80

mean = 1288

1048 1128 1208 1288 1368 1448 1528

Z = (X - mean)/sd = (X - 1288)/ 80

b)

P(X > 1250)

= 0.6826

1048 1128 1208 1288 1368 1448 1528

c)

P(X > x) = 0.375
P(Z > z) = 0.375
z = 0.385
hence
x = mean + z* sd
= 1288 + 0.385 * 80
= 1318.8

d)
sd(Xbar) = sd(X) /sqrt(n)

P(Xbar < 1225)
= P(Z < (1225 - 1288)/(80/sqrt(200))
= P(Z < -11.1369)
= 0

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