# MTH 147 FALL 2015 NAME___________________

MTH 147 Fall 2015 Name:___________________

MWF 8:05am 8:55am CSU ID:___________________

Homework 5

Due: October 28, 2015 IN CLASS

Instructions: Homework must be turned in at the start of class on the due date. Please see

syllabus for information about late homework. Read all questions carefully and present all

answers within the provided space. If the space is not enough you may attach a separate piece of

paper, which must contain your name, CSU ID and question number. All work must be shown

to receive full credit.

Total Points: 10

Question 1:

Use the provided normal distribution table to verify the probability of

a) 1.78 standard deviations above the mean of 5.6

b) 0.67 standard deviation below the mean of 5.6

c) Between 1.96 standard deviation above and below the mean of 5.6

Question 2:

Use the provided normal distribution table to find the z-score of

a) The lowest 2%

b) The highest 2%

Question 3:

Given a mean of 25 and a standard deviation of 5

a) What value corresponds to a z-score of -2.5?

b) What value corresponds to a z-score of 1.5?

c) What value corresponds to the cumulative proportion of 65%?

Question 4:

A new roller coaster at Cedar Point requires individuals to be at least 52” (62 inches) tall to ride.

It is estimated that the heights of 10 year-old-kids are normally distributed with mean of 54.5

inches and standard deviation of 5 inches.

a) What proportion of 10 year-old-kids is tall enough to ride the coaster?

b) A smaller coaster has a height requirement of 40 inches to ride. What proportion of 10

year-old-kids is tall enough to ride this coaster?

c) What proportion of 10 year-old-kids is tall enough to ride the coaster in part b but not tall

enough to ride the coaster in part a?

Question 5:

The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a

standardized measure used in observing infants over time. It is approximately normal with a

mean of 168 and a standard deviation of 21.

a) What proportion of children has an MDI of (i) at least 145? (ii) at least 200?

b) Find the MDI score that is the 80% percentile.

c) Find the MDI score such that only 1.5% of the population has MDI below it.