1)The heights of students at a college are normally distributed with a mean of 1

Question

1)The heights of students at a college are normally distributed with a mean of 175 cm and a standard deviation of 6 cm. One might expect in a sample of 1000 students that the number of students with heights less than 163 cm is: a) 456 b) 23 c) 228d) 997 e) 477

2)The grades on a statistics test are normally distributed with a mean of 62 and Q1=52. If the instructor wishes to assign B's or higher to the top 30% of the students in the class, what grade is required to get a B or higher? (Round your answer to two decimal places)

3)The run times of a marathon runner are approximately normally distributed. The z-score for his run this week is – 2 . Which one of the following statements is a correct interpretation of his z-score?

This week his time was 2 (standard deviation/minutes?) (lower or higher?) than his (time last week/average time/ best time ever?)

4)The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points.

(a) What proportion of the students scored at least 21 points on this test, rounded to five decimal places?

(b) What is the 31 percentile of the distribution of test scores, rounded to three decimal places?

5)The Environmental Protection agency requires that the exhaust of each model of motor vehicle be tested for the level of several pollutants. The level of oxides of nitrogen (NOX) in the exhaust of one light truck model was found to vary among individually trucks according to a Normal distribution with mean 1.45 grams per mile driven and standard deviation 0.40 grams per mile.

(a) What is the 20th percentile for NOX exhaust, rounded to four decimal places?

(b) Find the interquartile range for the distribution of NOX levels in the exhaust of trucks rounded to four decimal places.

6) A study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. It was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 1.25 days with an approximately normal distribution.

(a) Find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places.

(b) Find the probability that their hospital stay is greater than 6 days, rounded to five decimal places.

Explanation / Answer

HERE THE DISTRIBUTION OF HEIGHT FOLLOWS NORMAL WITH MEAN 175 ANS STANDARD DEVIATION 6

SO P(X<163) WHEN X~N(175,6)

P(X<163) IS GIVEN BY THE COMMAND pnorm(163,175,6)

WHICH IS 0.02275013

SO P(X<163) IS 0.02275013

SO OUT OF 1000, 1000*0.02275013=22.75013=23

OPTION B 23 ANS .

NOTE:ACCORDING TO CHEGG'S POLICY ONE QUESTION IN ONE POST IS SUGGESTED.

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