Answer :
The probability that the average score for the week is between 220 and 228 = 0.7641
Susan's score on bowling follows Normal Distribution.
Average score or mean, μ = 225
Standard Deviation, σ = 13
Number of times Susan bowled, n = 16
Since the scores follows Normal Distribution, the z-score = (x-μ)√n/σ
When the score, x = 220,
z = (220-225)√16/13
= -20/13
= -1.538
When the score, x = 228,
z = (228-225)√16/13
= 12/13
=0.923
Hence The probability that the average score for the week is between 220 and 228 = P(220 < x < 228)
= P(-1.538 < z < 0.923)
= P(z < 0.923) - P(z < -1.538)
= (0.5 + 0.3212) -( 0.5 - 0.4429) [From the z-tables]
= 0.7641
The question is incomplete. Find the complete question below:
Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. If during a typical week Susan bowls 16 games, what is the probability that her average score for the week is between 220 and 228?
Learn more about normal distribution at https://brainly.com/question/4079902
#SPJ4
