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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

According to National Vital Statistics, the average length of a newborn baby is \(19.5\) inches with a standard deviation of \(0.9\) inches. The distribution of lengths is approximately Normal. Use technology or a table to answer these questions. For each include an appropriately labeled and shaded Normal curve. a. What is the probability that a newborn baby will have a length of 18 inches or less? b. What percentage of newborn babies will be longer than 20 inches? c. Baby clothes are sold in a "newborn" size that fits infants who are between 18 and 21 inches long. What percentage of newborn babies will not fit into the "newborn" size either because they are too long or too short?

According to the National Health Center, the heights of 6 -year-old girls are Normally distributed with a mean of 45 inches and a standard deviation of 2 inches. a. In which percentile is a 6 -year-old girl who is \(46.5\) inches tall? b. If a 6 -year-old girl who is \(46.5\) inches tall grows up to be a woman at the same percentile of height, what height will she be? Assume women are distributed as \(N(64,2.5)\).

According to dogtime .com, the mean weight of an adult St. Bernard dog is 150 pounds. Assume the distribution of weights is Normal with a standard deviation of 10 pounds. a. Find the standard score associated with a weight of 170 pounds. b. Using the Empirical Rule and your answer to part a, what is the probability that a randomly selected St. Bernard weighs more than 170 pounds? c. Use technology to confirm your answer to part \(\mathrm{b}\) is correct. d. Almost all adult St. Bernard's will have weights between what two values?

Scores in Florida According to the 2017 SAT Suite of Assessments Annual Report, the average ERW (English, Reading, Writing) SAT score in Florida was 520 . Assume the scores are Normally distributed with a standard deviation of 100 . Answer the following including an appropriately labeled and shaded Normal curve for each question. a. What is the probability that an ERW SAT taker in Florida scored 500 or less? b. What percentage of ERW SAT takers in Florida scored between 500 and 650 ? c. What ERW SAT score would correspond with the 40 th percentile in Florida?

In a standard Normal distribution, if the area to the left of a z-score is about \(0.6666\), what is the approximate z-score? First locate, inside the table, the number closest to \(0.6666 .\) Then find the z-score by adding \(0.4\) and \(0.03\); refer to the table. Draw a sketch of the Normal curve, showing the area and the \(z\) -score.
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