A study of able-bodied female students at the University of Illinois found that their times for...

A study of able-bodied female students at the University of Illinois found that their times for the mile run were approximately normal with mean 7.11 minutes and standard deviation 0.74 minutes.

(a) Choose a student at random from this group and call her time for the mile X. What is the probability her mile run time was no more than 6 minutes? Sketch a graph of this situation and shade the appropriate region.

(b) What is the probability that exactly 2 out of 5 randomly selected females in the study will run the mile in less than 6 minutes?

Solutions

Expert Solution

Let X : time required to run a mile.

Probability that a randomly selected girl will run a mile in less than 6 minutes is,

0.0668

We need to calculate that exactly 2 girls run a mile in less than 6 minutes and hence the 3 other girls will take more than 6 minutes to run a mile.

Hence the probability we need to calculate is,

P(X1<=6,X2<=6,X3>6,X4>6,X5>6)

=P(X<=6) *P(X<=6) * P(X>6) * P(X>6) * P(X>6)

(Since the time to run a mile for each girl is independent of othe other girl

And X is identical random variable hence follows identical normal distribution.)

The probability of exactly 2 girls run within 6 minutes out of 5 is

0.0004

orchestra answered 1 year ago

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