Can you explain the answer? Why is it not a normal distribution? Also, shouldn\'

Question

Can you explain the answer? Why is it not a normal distribution?

Also, shouldn't the conclusion be that 15.87% of the people ran the marathon slower than she did, not "faster"?

15. Amy ran a marathon in 3.6 hours. The mean time is 4.4 with a standard deviation of 0.8 hours. She calculates her z-score to be -1.0 and looks at a z-table and sees that 15.87% of the values are below-1.0. Thus, she concludes that 15.87% of the people ran the marathon faster than she is. There is an error in Amy's logic. What is it?

Explanation / Answer

here the z-score is z=(x-mean)/sd=(3.6-4.4)/0.8=-1

P(X<3.6)=P(Z<-1)=0.1587,

So her logic that 15.87% of the pople ran the marathon faster than she is , not true. in fact this value should be 100-15.87%=84.13%

In other way this imply that Amy is faster than 15.87% of the people ran the marathon.

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