Alexus Deleon
2022-09-21
Answered

Assume normal distributions in the following exercises. Find the value of z. An estimated 86% of the scores are to the left of z.

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Abram Jacobson

Answered 2022-09-22
Author has **8** answers

The z-score represents the number of standard deviations between an observation and the mean. Whatever scale is used for on a normal curve, we can associate a value of z with each value of x.

We use z to find the area under the normal curve between two scores. To do so, we use the standard normal table. The table gives area between the mean and a z-score for selected z-scores.So as 86% of the result is to the left of z, and the normal distribution is symmetric with the area below the normal curve 1, is 0.5 on the left and right sides of the mean. This actually means that between z and the mean is 36%, so the area between z and the mean is 0.42. Using the table of standard normal distribution we can see that the area A = 0.36 corresponds to z = 1.09.

We use z to find the area under the normal curve between two scores. To do so, we use the standard normal table. The table gives area between the mean and a z-score for selected z-scores.So as 86% of the result is to the left of z, and the normal distribution is symmetric with the area below the normal curve 1, is 0.5 on the left and right sides of the mean. This actually means that between z and the mean is 36%, so the area between z and the mean is 0.42. Using the table of standard normal distribution we can see that the area A = 0.36 corresponds to z = 1.09.

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Describe in words the surface whose equation is given. (assume that r is not negative.) $\theta =\frac{\pi}{4}$

a) The plane$y=-z$ where y is not negative

b) The plane$y=z$ where y and z are not negative

c) The plane$y=x$ where x and y are not negative

d) The plane$y=-x$ where y is not negative

e) The plane$x=z$ where x and y are not negative

a) The plane

b) The plane

c) The plane

d) The plane

e) The plane

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Explain why t distributions tend to be flatter and more spread out than the normal distribution.

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The manager of the store in the preceding exercise calculated the residual for each point in the scatterplot and made a dotplot of the residuals.

The distribution of residuals is roughly Normal with a mean of $0 and standard deviation of $22.92.

The middle 95% of residuals should be between which two values? Use this information to give an interval of plausible values for the weekly sales revenue if 5 linear feet are allocated to the stores

The distribution of residuals is roughly Normal with a mean of $0 and standard deviation of $22.92.

The middle 95% of residuals should be between which two values? Use this information to give an interval of plausible values for the weekly sales revenue if 5 linear feet are allocated to the stores

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asked 2022-03-23

Assume that females have pulse rates that are normally distributed with a mean of

μ=74.0

beats per minute and a standard deviation of

σ=12.5

beats per minute. Complete parts (a) through (c) below.

Part 1

**a.** If 1 adult female is randomly selected, find the probability that her pulse rate is between

68

beats per minute and

80

beats per minute.

The probability is

enter your response here.

(Round to four decimal places as needed.)

Part 2

**b.** If

16

adult females are randomly selected, find the probability that they have pulse rates with a mean between

68

beats per minute and

80

beats per minute.

The probability is

enter your response here.

(Round to four decimal places as needed.)

Part 3

**c.** Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

**A.**

Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size.

**B.**

Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size.

**C.**

Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size.

**D.**

Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

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A city recreation department offers Saturday gymnastics classes for beginning and advanced students. Each beginner class enrolls 15 students, and each advanced class enrolls 10 students. Available teachers, space, and time lead to the following constraints. ∙∙ There can be at most 9 beginner classes and at most 6 advanced classes. ∙∙ The total number of classes can be at most 7. ∙∙ The number of beginner classes should be at most twice the number of advanced classes.
a. What are the variables in this situation?
b. Write algebraic inequalities giving the constraints on the variables.
c. The director wants as many children as possible to participate. Write the objective function for this situation.
d. Graph the constraints and outline the feasible region for the situation.
e. Find the combination of beginner and advanced classes that will give the most children a chance to participate.
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