The heights of kindergartners at a local school are approximately normally distr

Question

The heights of kindergartners at a local school are approximately normally distributed, with amean of 40.0 inches and a standard deviation of 2.3 inches?

a. What is the probability that a randomly selected kindergartener is at least 35 inches tall?

b.What is the probabilty that a randomly selected kindergartener is between 37.9and 41.5 inches tall?

c. What is the probability that in a randomly selected sample of 17 kindergarteners, their mean height is more than 39 inches?

d. The parents of a kindergartener at the schoolare told that their daughter is at the 75th percentile in height. What is her height in inches? (round to the nearest tenth of an inch)

e. What is the probability that a randomly selected kindergartners excactly 40.34294 inches?

Explanation / Answer

a)P(X>35)=1-P(X<35)=1-P(Z<(35-40)/2.3)=1-P(Z<-2.1739)=1-0.0149=0.9851

b)P(37.9<X<41.5)=P(-0.9130<Z<0.6522)=0.7429-0.1806=0.5622

c)for n=17; std error of mean =std deviation/(n)1/2 =0.5578

P(X>39)=1-P(X<39)=1-P(Z<-1.7927)=1-0.0365=0.9635

d) for 75th percentile; z=0.6745

hence corresponding height =40+0.6745*2.3=41.55

e)P(X=40.34)=0 ; as probabilty of a point is 0 for continuous distribution function is 0.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.