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Chapter 6: Problem 23

Find the following probabilities for the standard normal distribution. a. \(P(z<-2.34)\) b. \(P(.67 \leq z \leq 2.59)\) c. \(P(-2.07 \leq z \leq-.93)\) d. \(P(z<1.78)\)

Short Answer

Expert verified
The probabilities for the given z-scores are as follows: a) P(z<-2.34) = 0.0094, b) P(.67 鈮� z 鈮� 2.59) = 0.9951 - 0.7486 = 0.2465, c) P(-2.07 鈮� z 鈮� -0.93) = 0.1753 - 0.0192 = 0.1561, d) P(z<1.78) = 0.9625

Step by step solution

01

Understand the notations and the Problem

In the standard normal distribution, 'z' is the number of standard deviations from the mean. P(z<a) represents the probability that the z-value is less than 'a', P(a鈮鈮) represents the probability that the z-value is between 'a' and 'b'. These probability values can be found using the standard normal distribution table.
02

Find the probability for P(z

Look up the z-score in the standard normal distribution table. For the z-score of -2.34, the corresponding probability is 0.0094
03

Calculate the probability for P(.67 鈮� z 鈮� 2.59)

This requires calculating the probabilities for the range encompassed by z-scores of 0.67 and 2.59. On the standard normal distribution table, find the probabilities for these scores - P(z<0.67) is 0.7486, P(z<2.59) is 0.9951. Subtract P(z<0.67) from P(z<2.59) to get the cumulative probability within this range.
04

Calculate the probability for P(-2.07 鈮� z 鈮� -0.93)

On the standard normal distribution table, find the probabilities for z-scores -2.07 and -0.93. P(z<-2.07) is 0.0192, P(z<-0.93) is 0.1753. Subtract P(z<-2.07) from P(z<-0.93) to get the cumulative probability within this range.
05

Find the probability for P(z

Look up the z-score of 1.78 in the standard normal distribution table. The corresponding probability is 0.9625

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Most popular questions from this chapter

According to a Gallup poll, \(92 \%\) of Americans believe in God (Time, June 20,2011 ). Suppose that this result is true for the current population of adult Americans. What is the probability that the number of adult Americans in a sample of 500 who believe in God is a. exactly 445 b. at least 450 c. 440 to 470

Determine the following probabilities for the standard normal distribution. a. \(P(-1.83 \leq z \leq 2.57)\) b. \(P(0 \leq z \leq 2.02)\) c. \(P(-1.99 \leq z \leq 0)\) d. \(P(z \geq 1.48)\)

What is the difference between the probability distribution of a discrete random variable and that of a continuous random variable? Explain.

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Find the area under the standard normal curve a. from \(z=0\) to \(z=2.34\) b. between \(z=0\) and \(z=-2.58\) c. from \(z=.84\) to \(z=1.95\) d. between \(z=-.57\) and \(z=-2.49\) e. between \(z=-2.15\) and \(z=1.87\)
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