Recently, the bowling scores of a certain bowler were normally distributed with

Question

Recently, the bowling scores of a certain bowler were normally distributed with mean 209 and standard deviation 19 a) Find the probability that a score is from 195 to 215, and interpret your results. b) Find the probability that a score is from 170 to 185, and interpret your results. c) Find the probability that a score is greater than 205, and interpret your results. Click the icon to view the standard normal distribution table. a) The probability that a score is from 195 to 215 is (Round to four decimal places as needed.) Interpret your results. Select the correct choice below and fill in the answer box to complete your choice Round to the nearest whole number as needed.) O A. About % of the bowler's scores are between 195 and 205. O B. About % of the bowler's scores are between 205 and 215. ° C. About % of the bowler's scores are between 195 and 215. b) The probability that a score is from 170 to 185 is Round to four decimal places as needed.) nterpret your results. Select the correct choice below and fill in the answer box to complete your choice

Explanation / Answer

a)

P(195 < X<215) = P(X < 215) - P(X < 195)

= P(Z < 215-209/19) - P(Z < 195-209/19)

= P(Z < 0.3158) - P(Z < -0.7368)

= 0.6239 - 0.2306

= 0.3933

b)

P(170 < X<185) = P(X < 185) - P(X < 170)

= P(Z < 185-209/19) - P(Z < 170-209/19)

= P(Z < -1.2632) - P(Z < -2.0526)

=0.1033 - 0.0201

= 0.0832

c)

P(X >205) = P(Z > 205 - 209/19)

= P(Z > -0.2105)

= 0.5834

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