Need help with a through f, thanks! EXERCISE 18 A previous year, the weights of
ID: 3305243 • Letter: N
Question
Need help with a through f, thanks!
EXERCISE 18 A previous year, the weights of the members of the San Francisco 49ers and the Dallas Cowboys were published in the San Jose Mercury News. The factual data are compiled into the following table Shirt# 210 211-250 251-290 290 1-33 2 5 34-66 16 18 66-99 6 TABLE 4 12 For the following, suppose that you randomly select one player from the 49ers or Cowboys. a. Find the probability that his shirt number is from 1 to 33. b. Find the probability that he weighs at most 210 pounds. c. Find the probability that his shirt number is from 1 to 33 AND he weighs at most 210 pounds d. Find the probability that his shirt number is from 1 to 33 OR he weighs at most 210 pounds. e. Find the probability that his shirt number is from 1 to 33 GIVEN that he weighs at most 210 pounds. f. If having a shirt number rom 1 o 33 and weighing at most 210 pounds were independent events, then what should be rue a utP irta 1 3 210 ou nas ?Explanation / Answer
Total frequency here is computed as = 21 + 5 + 6 + 18 + 7 + 4 + 6 + 12 + 22 + 5 = 106
a) Probability that his shirt number is from 1 to 33 is computed as:
= ( Frequency that his shirt number is from 1 to 33 ) / Total Frequency
= ( 21 + 5 ) / 106
= 0.2453
Therefore 0.2453 is the required probability here.
b) Probability that he weighs at most 210 pounds is computed as:
= ( Frequency that the weight is at most 210 pounds ) / Total frequency
= ( 21 + 6 + 6 ) / 106
= 0.3113
Therefore 0.3113 is the required probability here.
c) Probability that the shirt number is from 1 to 33 and he weighs at most 210 pounds is computed as:
= ( Frequency that the shirt number is from 1 to 33 and he weighs at most 210 pounds ) / Total frequency
= 21/ 106
= 0.1981
Therefore 0.1981 is the required probability here.
d) Probability that his shirt number is from 1 to 33 or he weighs at most 210 pounds is computed as:
= ( 21 + 6 + 6 + 5) / 106
= 0.3585
Therefore 0.3585 is the required probability here.
e) Probability that the shirt number is from 1 to 33 given that he weighs at most 210 pounds is computed using Bayes theorem as:
= Probability that the shirt number is from 1 to 33 and he weighs at most 210 pounds / Probability that he weighs at most 210 pounds
= 0.1981 / 0.3113
= 0.6364
Therefore 0.6364 is the required probability here.
f) If the 2 events are independent events, then
P( shirt #1-33 | < 210 pounds ) = P( shirt #1-33 )