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Chapter 6: Problem 46

Assume a standard Normal distribution. Draw a separate, well-labeled Normal curve for each part. a. Find an approximate \(z\) -score that gives a left area of \(0.7000\). b. Find an approximate \(z\) -score that gives a left area of \(0.9500\).

Short Answer

Expert verified
The approximate \(z\)-scores that give a left area of \(0.7000\) and \(0.9500\) respectively are generally found to be \(0.52\) and \(1.65\), although some variations might be there based on the level of approximation.

Step by step solution

01

Finding the z-score for left area 0.7000

For the first part, you'll use the standard Normal distribution table or Z-table or modern statistical software to determine the \(z\)-score. This is done by looking up the area closest to \(0.7000\) in the body of the table and then finding the corresponding \(z\)-score.
02

Verifying z-score for left area 0.7000

After finding the z-score, verify it by ensuring that the area to the left of it on the standard Normal distribution curve is \(0.7000\), as per the problem's requirements.
03

Finding the z-score for left area 0.9500

For the second part, just like in step 1, you'll use the standard Normal distribution table or Z-table to find the \(z\)-score that gives a left-hand area of \(0.9500\). Again, this is done by looking up the area closest to \(0.9500\) in the body of the table and then finding the corresponding \(z\)-score.
04

Verifying z-score for left area 0.9500

After finding the z-score, verify it by ensuring that the area to the left of it on the standard Normal distribution curve is \(0.9500\), as per the problem's requirements.

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Most popular questions from this chapter

Toronto drivers have been going to small towns in Ontario (Canada) to take the drivers' road test, rather than taking the test in Toronto, because the pass rate in the small towns is \(90 \%\), which is much higher than the pass rate in Toronto. Suppose that every day, 100 people independently take the test in one of these small towns. a. What is the number of people who are expected to pass? b. What is the standard deviation for the number expected to pass? c. After a great many days, according to the Empirical Rule, on about 95\% of these days the number of people passing the test will be as low as _______ and as high as _______. d. If you found that on one day, 89 out of 100 passed the test, would you consider this to be a very high number?

Babies in the United States have a mean birth length of \(20.5\) inches with a standard deviation of \(0.90\) inch. The shape of the distribution of birth lengths is approximately Normal. a. How long is a baby born at the 20 th percentile? b. How long is a baby born at the 50 th percentile? c. How does your answer to part b compare to the mean birth length? Why should you have expected this?

A married couple plans to have four children, and they are wondering how many boys they should expect to have. Assume none of the children will be twins or other multiple births. Also assume the probability that a child will be a boy is \(0.50 .\) Explain why this is a binomial experiment. Check all four required conditions.

Whales have one of the longest gestation periods of any mammal. According to whalefacts.org, the mean gestation period for a whale is 14 months. Assume the distribution of gestation periods is Normal with a standard deviation of \(1.2\) months. a. Find the standard score associated with a gestational period of \(12.8\) months. b. Using the Empirical Rule and your answer to part a, what percentage of whale pregnancies will have a gestation period between \(12.8\) months and 14 months? c. Would it be unusual for a whale to have a gestation period of 18 months? Why or why not?

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