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Chapter 6: Problem 18

Obtain the area under the standard normal curve a. to the right of \(z=1.43\) b. to the left of \(z=-1.65\) c. to the right of \(z=-.65\) d. to the left of \(z=.89\)

Short Answer

Expert verified
The areas under standard normal curve: a. To the right of z=1.43 is 0.0764. b. To the left of z=-1.65 is 0.0495. c. To the right of z=-0.65 is 0.7422. d. To the left of z=0.89 is 0.8133.

Step by step solution

01

Obtain Probabilities for Given Z-Scores

To solve the problems, one must first find the probabilities corresponding to the given z-scores using the standard normal distribution table. This will give one the proportion of data below the given z-score (to the left). The values obtained are: a. 0.9236 for z=1.43 b. 0.0495 for z=-1.65 c. 0.2578 for z=-0.65 d. 0.8133 for z=0.89
02

Calculate Area under Curve using Formula

The area under the curve to the right of a given z-score equals 1 minus the cumulative probability of the z-score. On the other hand, the cumulative probability of the z-score itself gives the area under the curve to the left of the z-score. Based on that, calculate the areas: a. The area to the right of z=1.43 is \(1 - 0.9236 = 0.0764\). b. The area to the left of z=-1.65 is 0.0495. c. The area to the right of z=-0.65 is \(1 - 0.2578 = 0.7422\). d. The area to the left of z=0.89 is 0.8133.

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Most popular questions from this chapter

A study has shown that \(20 \%\) of all college textbooks have a price of \(\$ 184.52\) or higher. It is known that the standard deviation of the prices of all college textbooks is \(\$ 36.35 .\) Suppose the prices of all college textbooks have a normal distribution. What is the mean price of all college textbooks?

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