chapter 7 - statistics

Find the​ Z-scores that separate the middle 73​% of the distribution from the area in the tails of the standard normal distribution.

-1.1, 1.1

Find the​ Z-score such that the area under the standard normal curve to the left is 0.52.

0.05

The area under the normal curve to the right of μ equals​ _______.

0.5

Find the​ z-score such that the area under the standard normal curve to the right is 0.29.

0.55

Find the​ Z-score such that the area under the standard normal curve to the right is 0.11.

1.23

A study was conducted that resulted in the following relative frequency histogram. Determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.

The histogram is not bell-shaped, so a normal distribution could not be used as a model for the variable.

The points at x=​_______ and x=​_______ are the inflection points on the normal curve.

The points are x=μ−σ and x=μ+σ.

There are two college entrance exams that are often taken by​ students, the ACT and the SAT. The composite score on the ACT is approximately normally distributed with mean 21.1 and standard deviation 5.1. The composite score on the SAT is approximately normally distributed with mean 1026 and standard deviation 210. Suppose you scored 28 on the ACT and 1187 on the SAT. Which exam did you score better​ on? Justify your reasoning using the normal model.

The score on the ACT is​ better, because the percentile for the the ACT score is higher.

The graph to the right is the uniform probability density function for a friend who is x minutes late. ​(a) Find the probability that the friend is between 5 and 20 minutes late. ​(b) It is 10 A.M. There is a 30​% probability the friend will arrive within how many​ minutes?

a. 0.5 b. 9

A​ _______ is a graph that plots observed data versus normal scores.

normal probability plot

A normal score is the expected​ z-score of a data​ value, assuming the distribution of the random variable is normal. Is this statement true or​ false?

true

The notation zα is the​ z-score that the area under the standard normal curve to the right of zα is​ _______.

α

Find the value of zα. z0.05

(use statcrunch) 1.64

One graph in the figure represents a normal distribution with mean μ=10 and standard deviation σ=2.The other graph represents a normal distribution with mean μ=14 and standard deviation σ=2. Determine which graph is which and explain how you know.

Graph A has a mean of μ=10 and graph B has a mean of μ=14 because a larger mean shifts the graph to the right.

Determine whether the following graph can represent a normal curve.

No, because the graph is not always greater than or equal to zero

Suppose a sample of​ O-rings was obtained and the wall thickness​ (in inches) of each was recorded. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed.

Yes. The correlation between the expected ​z-scores and the observed ​data, 0.972​, exceeds the critical value, 0.941. Therefore, it is reasonable to conclude that the data come from a normal population