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Chapter 6: Problem 24

Find the following probabilities for the standard normal distribution. a. \(P(z<-1.31)\) b. \(P(1.23 \leq z \leq 2.89)\) c. \(P(-2.24 \leq z \leq-1.19)\) d. \(P(z<2.02)\)

Short Answer

Expert verified
The solutions are: a) 0.0951, b) 0.1071, c) 0.1046, d) 0.9783.

Step by step solution

01

Refer to the Z-Table

Consult a Z-table or an online calculator to find the values for the required probabilities. The Z-table tells you the probability that a randomly selected z score is less than or equal to a given z score.
02

Finding P(z < -1.31)

To find the probability for z less than -1.31, find the intersection point of row -1.3 and column 0.01 (since 1.31 is the same as 1.3 + 0.01) in the Z table. This gives a probability of 0.0951.
03

Finding P(1.23 鈮� z 鈮� 2.89)

To find the probability that 1.23 is less or equal to the z-score that is less than or equal to 2.89, subtract the two respective probabilities found from the z-tables. These probabilities will be 0.8910 and 0.9981 respectively. So subtracting these will yield 0.1071.
04

Finding P(-2.24 鈮� z 鈮� -1.19)

To find the probability that -2.24 is less or equal to the z-score and is less than or equal to -1.19, subtract the two respective probabilities from the z-tables. These probabilities will be 0.0125 and 0.1171 respectively. So subtracting these will yield 0.1046.
05

Finding P(z < 2.02)

To find the probability for z less than 2.02, find the intersection point of row 2.0 and column 0.02 (since 2.02 is the same as 2.0 + 0.02) in the Z table. This gives a probability of 0.9783.

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Most popular questions from this chapter

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