Over the past 10 years, the local school district has measured physical fitness

Question

Over the past 10 years, the local school district has measured physical fitness for all high school freshmen. During that time, the average score on a treadmill endurance task has been mu = 19.8 minutes with a standard deviation sigma = 7.2 minutes. Assuming that the distribution is approximately normal, find each of the following probabilities. What is the probability of randomly selecting a student with a treadmill time greater than 25 minutes? If the school required a minimum time of 10 minutes for students to pass the physical education course, what proportion of the freshmen would fail?

Explanation / Answer

here from normal distribution zscore =(X-mean)/std deviation

a) P(X>25) =1-P(X<25) =1-P(Z<(25-19.8)/7.2)=1-P(Z<0.7222)=1-0.7649=0.2351

b)P(X<10) =P(Z<(10-19.8)/7.2)=P(Z<-1.3611)=0.0867

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