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Every day Cara runs for five miles

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Every day Cara runs for five miles. Suppose that the time it takes her to complete the run is a random variable that is normally distributed with a mean of 50 minutes and a standard deviation of 5 minutes. Today Cara ran the five miles in 46 minutes. What is the probability that she will beat her time tomorrow?

 

A person must score in the upper 2% of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for Mensa?

 

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