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Chapter 2: Q 2.1. (page 91)

Lynette, a student in the class, is 65 inches tall. Find and interpret her z-score.

Short Answer

Expert verified

z鈭�score is the鈭�0.466.

Step by step solution

01

Step 1. Given

A dot plot shows the height distribution in the class, as well as summary data from the computer output.

02

Step 2. Concept

Value that has been standardized (z-score) The standardized value of xis z=x-meanstandarddeviationif xis an observation from a distribution with known mean and standard deviation. A z-score is a term used to describe a standardized value.

03

Step 3. Explanation

If xis an observation from a distribution that has known mean and standard deviation, standardized score forxis,

z=x鈭�meanstandarddeviation

So here, x=65

And from the given dot plot x=67and standard deviation is Sx=4.09

z=65-674.29

z=-0.466

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Most popular questions from this chapter

Brent is a member of the school鈥檚 basketball team. The mean height of the players on the team is 76 inches. Brent鈥檚 height translates to a z-score of 鈭�0.85 in the team鈥檚 height distribution. What is the standard deviation of the team members鈥� heights?

Tall or short? Mr. Walker measures the heights (in inches) of the students in one of his classes.

He uses a computer to calculate the following numerical summaries: Next, Mr. Walker has his entire class stand on their chairs, which are 18 inches off the ground. Then he measures the distance from the top of each student鈥檚 head to the floor.

(a) Find the mean and median of these measurements. Show your work.

(b) Find the standard deviation and IQR of these measurements. Show your work.

T2.5. The average yearly snowfall in Chillyville is Normally distributed with a mean of 55 inches. If the snowfall in Chillyville exceeds 60inches in 15% of the years, what is the standard deviation?
(a) 4.83 inches
(d) 8.93 inches
(b) 5.18 inches
(c) The standard deviation
(c) 6.04 inches cannot be computed from the given information.

R2.8 Working backward

(a) Find the number zat the 80th percentile of a standard Normal distribution.

(b) Find the number localid="1649404103275" zsuch that localid="1649404108890" 35%of all observations from a standard Normal distribution are greater than localid="1649404115271" z.

- Use Table A to find the percentile of a value from any Normal distribution and the value that corresponds to a given percentile.

If Mrs. Navard had the entire class stand on a 6-inch-high platform and then had the students measure the distance from the top of their heads to the ground, how would the shape, center, and spread of this distribution compare with the original height distribution?

See all solutions

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