A popular video game claims that the average time needed to reach level 10 Paladin is 3 hours with a standard deviation of 0.4 hours. James thinks that he and his four friends are more skilled than the average gamer because it took them an average of only 2.5 hours. Which of the following is the most restrictive level that would validate his claim?

1%

2.5%

5%

10%

Question

Jeremiah Mckinney

Mathematics

2 July, 16:51

A popular video game claims that the average time needed to reach level 10 Paladin is 3 hours with a standard deviation of 0.4 hours. James thinks that he and his four friends are more skilled than the average gamer because it took them an average of only 2.5 hours. Which of the following is the most restrictive level that would validate his claim?

1%

2.5%

5%

10%

+3

Answers (1)

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Jordon Mitchell · Answer 1

In this case, it is equal to 0.178. The z-score is defined the distance from the sample to the population means in units of standard error. z = (3 - 2.5) / 0.178 = 2.81 at this z-score, the probability is 0.9974 so A=1%