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Chapter 6: Q.40 (page 386)

About what percent of x values lie between the first and third standard deviations(both sides)?

Short Answer

Expert verified

About 32% of the x values from normal distribution will lie between first and third standard deviation.

Step by step solution

01

Given information

Given in the question that, We have to find the percent of xvalues lie between the first and third standard deviations(both sides).

02

Explanation

According to the empirical rule of normal distribution, within one standard deviation of the mean, there are approximately 68%values of xlies and within three standard deviations of the mean, there are approximately 99.7%values of xlies. So, the percent of the xvalues from normal distribution lie between first and third standard deviation from the mean will be:

=99.7%−68%

=31.7%

≈32%

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Most popular questions from this chapter

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days.

a. In words, define the random variable X.

b. X ~ _____(_____,_____)

c. If one of the trials is randomly chosen, find the probability that it lasted at least 24 days. Sketch the graph and write the probability statement.

d. Sixty percent of all trials of this type are completed within how many days?

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3days and a standard deviation of 2.1days.

The 90thpercentile for recovery times is

a. 8.89

b. 7.07

c. 7.99

d. 4.32

Use the following information to answer the next four exercises:

X~N(54,8)

Find the probability thatx>56.

In 2012, 1,664,479 students took the SAT exam. The distribution of scores in the verbal section of the SAT had a mean µ=496 and a standard deviation σ=114. Let X = a SAT exam verbal section score in 2012. Then X~N(496,114). Find the z-scores for x1=325 andx2=366.21. Interpret each z-score. What can you say about x1=325 and x2=366.21 as they compare to their respective means and standard deviations ?

What is the area to the right of one?
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