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Z-Scores. Find the z-scores that contain the middle 78% of the standard normal distribution's area. Please provide a sketch that illustrates your answer. Be sure to write down Statcrunch or calculator inputs used.

 

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Priyanshu Patel
Priyanshu PatelLv10
25 Feb 2021
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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

Find the indicated z -score. Be sure to draw a standard normal curve that depicts the solution. Find z-scores that separate the middle 99% of the distribution from the area in the tails of the standard normal distribution.

Module 4 Minitab Assignment

Instructions:

Below you will find questions. Please use the provided data to complete the tasks and to answer the questions.

For the standard normal distribution, Z, find the proportion (percentage) of observations that satisfies each of the following statements. In each case, use a graph of the Normal curve and shade the area under the curve that is the answer to the question. 


Values of z larger than 2.33.

Between z = −1.50 and z = 1.18. 

Values of z less than 1.19. 

A set of final examination grades in an introductory statistics course was found to be normally distributed with a mean of 77 and a standard deviation of 8. For each of the following produce a normal distribution plot showing the appropriate shaded area.

What percentage of students scored lower than 70 on this exam? 

What percentage of students scored between 81 and 89? 

What percentage of students scored higher than 90 on this exam? 

What is the 80th percentile of scores? 

What is the 95th percentile of scores?

1. In its standardized form, the normal distribution 

(a) has a mean of 0 and a standard deviation of 1.

(b) has a mean of 1 and a variance of 0.

(c) has an area equal to 0.5.

(d) cannot be used to approximate discrete probability distributions.

 

2. For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3770.

The value of Z is

(a) 0.18

(b) 0.81

(c) 1.16

(d) 1.47

 

3. For some value of z, the probability that a standard normal variable is below z is 0.2090. The value of Z is 

(a) -0.81

(b) -0.31

(c) 0.31

(d) 1.96

 

4. For some positive value of X, the probability that a standard normal variable is between 0 and +2x is 0.1255.

The value of X is 

(a)  0.99

(b) 0.40

(c) 0.32

(d) 0.16

 

5. If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 35. minutes and a standard deviation of minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.

(a) 0.3551

(b) 0.3085

(c) 0.2674

(d) 0.1915 

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