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Answer:
N(AUC∩B') = 121
The number of students that like Reese's Peanut Butter Cups or Snickers, but not Twix is 121
Step-by-step explanation:
Let A represent snickers, B represent Twix and C represent Reese's Peanut Butter Cups.
Given;
N(A) = 150
N(B) = 204
N(C) = 206
N(A∩B) = 75
N(A∩C) = 100
N(B∩C) = 98
N(A∩B∩C) = 38
N(Total) = 500
How many students like Reese's Peanut Butter Cups or Snickers, but not Twix;
N(AUC∩B')
This can be derived by first finding;
N(AUC) = N(A) + N(C) - N(A∩C)
N(AUC) = 150+206-100 = 256
Also,
N(A∩B U B∩C) = N(A∩B) + N(B∩C) - N(A∩B∩C) = 75 + 98 - 38 = 135
N(AUC∩B') = N(AUC) - N(A∩B U B∩C) = 256-135 = 121
N(AUC∩B') = 121
The number of students that like Reese's Peanut Butter Cups or Snickers, but not Twix is 121
See attached venn diagram for clarity.
The number of students that like Reese's Peanut Butter Cups or Snickers, but not Twix is the shaded part
The empirical rule says that approximately 68% of any normal distributed data set lies within one standard deviation of the mean.
The same rule states that about 95% lies within two standard deviations of the mean. Using this rule, and the fact that any normal distribution is symmetric about its mean, you have