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Chapter 6: Problem 44

In a standard Normal distribution, if the area to the left of a \(z\) -score is about \(0.1000\), what is the approximate \(z\) -score?

Short Answer

Expert verified
The approximate z-score for an area of \(0.1000\) to its left in the standard Normal distribution is \(-1.28\).

Step by step solution

01

Understanding the Problem

We are asked to find the z-score which leaves an area of 0.1000 to its left in the standard Normal distribution. Area under the curve is also known as cumulative probability. In this case, the cumulative probability is given and we need to find the corresponding z-score.
02

Using the Z table or Calculator

A Z table or a calculator with a Z-distribution function allows us to find the z-score associated with a given area to the left of the score. For an area of \(0.1000\) to the left of the z-score, we look up \(0.1000\) in the body of the Z table or use the calculator function to find the corresponding z-score.
03

Finding the Z-Score

The z-score associated with a left-tail area of \(0.1000\) is about \(-1.28\). This means that approximately \(10\%\) of all data values are less (to the left) than this z-score in a standard Normal distribution.

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Most popular questions from this chapter

A 2017 Pew Research Center report on drones found that only \(24 \%\) of Americans felt that drones should be allowed at events, like concerts or rallies. Suppose 100 Americans are randomly selected. a. What is the probability that exactly 25 believe drones should be allowed at these events? b. Find the probability that more than 30 believe drones should be allowed at these events. c. What is the probability that between 20 and 30 believe drones should be allowed at these events? d. Find the probability that at most 70 do not believe drones should be allowed at these events.

Quantitative S \(\Lambda\) T scores are approximately Normally distributed with a mean of 500 and a standard deviation of 100 . Choose the correct StatCrunch output for finding the probability that a randomly selected person scores less than 450 on the quantitative SAT and report the probability as a percentage rounded to one decimal place.

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 \(0.9500\).

The distribution of white blood cell count per cubic millimeter of whole blood is approximately Normal with mean 7500 and standard deviation 1750 for healthy patients. 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 randomly selected person will have a white blood cell count between 6000 and \(10,000 ?\) b. An elevated white blood cell count can be a sign of infection somewhere in the body. A white blood cell count can be considered elevated if it is over 10,500 . What percentage of people have white blood cell counts in this elevated range? c. A white blood cell count below 4500 is considered low. People in this range may be referred for additional medical testing. What is the probability that a randomly selected person has a white blood cell count below \(4500 ?\)

The distribution of grade point averages GPAs for medical school applicants in 2017 were approximately Normal, with a mean of \(3.56\) and a standard deviation of \(0.34\). Suppose a medical school will only consider candidates with GPAs in the top \(15 \%\) of the applicant pool. An applicant has a GPA of \(3.71\). Does this GPA fall in the top \(15 \%\) of the applicant pool?
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