Q: Which of the following is the correct input for finding $$P(z \u003c 1.2)$$ using the $$\text{normalcdf}$$ function on a TI-84 calculator?

$$\text{normalcdf}(-100, 1.2, 0, 1)$$

Question 1

Suppose the heights of adult males are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What is the probability that a randomly selected male is taller than 76 inches? Use the standard normal distribution and appropriate calculator functions.

Accepted Answer

$$0.0228$$

Question 2

Given $$P(z \u003c a) = 0.95$$, what is the value of $$a to $$two decimal places? Use the inverse normal function.

Accepted Answer

$$a = 1.64$$

Question 3

A medical test result is considered positive if the z-score is greater than 2. What is the probability that a randomly selected test result from a standard normal distribution is positive?

Accepted Answer

$$0.0228$$

Question 4

If $$P(z \u003c -1.5) is $$required for a quality control process, what is the probability that a randomly selected item falls below this z-score?

Accepted Answer

$$0.0668$$

Question 5

A university entrance exam is normally distributed with mean $$500$$ and standard deviation $$100. $$What score corresponds to the top $$5\% of $$all test-takers?

Accepted Answer

$$664$$

Question 6

Which calculator function would you use to find the z-score corresponding to a given cumulative probability?

Accepted Answer

$$	ext{invNorm}$$

Question 7

If $$P(1 \u003c z \u003c 2)$$, what is the probability that a randomly selected value from a standard normal distribution falls between $$z = 1$$ and $$z = 2$$?

Accepted Answer

$$0.1359$$

Question 8

A pharmaceutical company wants to know the probability that a drug's effect falls between $$z = -2$$ and $$z = 1. $$What is this probability?

Accepted Answer

$$0.8186$$

Question 9

If $$P(z \u003e a) = 0.10$$, what is the value of $$a$$?

Accepted Answer

$$a = 1.28$$

Question 10

A researcher finds that $$P(z \u003c b) = 0.025. $$What is the value of $$b$$?

Accepted Answer

$$b = -1.96$$

Question 11

Which of the following best describes the use of the $$	ext{normalcdf}$$ function on a TI-84 calculator?

Accepted Answer

It calculates the probability between two z-scores.

Question 12

A hospital records the recovery times of patients and finds they are normally distributed with mean $$8$$ days and standard deviation $$2$$ days. What is the probability that a patient recovers in less than $$5$$ days?

Accepted Answer

$$0.0668$$

Question 13

If $$P(z \u003c c) = 0.80$$, what is the value of $$c$$?

Accepted Answer

$$c = 0.84$$

Question 14

A company wants to ensure that only the top $$2.5\% of $$applicants are selected based on a test score that is normally distributed. What z-score cutoff should they use?

Accepted Answer

$$z = 1.96$$

Question 15

If $$P(z \u003c d) = 0.01$$, what is the value of $$d$$?

Accepted Answer

$$d = -2.33$$

Question 16

A student scores $$1.5$$ standard deviations above the mean on a standardized test. What percentage of students scored lower than this student?

Accepted Answer

$$93.32\%$$

Question 17

Which of the following is the correct input for finding $$P(z \u003c 1.2)$$ using the $$	ext{normalcdf}$$ function on a TI-84 calculator?

Accepted Answer

$$	ext{normalcdf}(-100, 1.2, 0, 1)$$

Question 18

A psychologist wants to know the probability that a randomly selected person scores between $$z = -1$$ and $$z = 1 on a $$personality test. What is this probability?

Accepted Answer

$$0.6826$$

Question 19

If $$P(z \u003e e) = 0.025$$, what is the value of $$e$$?

Accepted Answer

$$e = 1.96$$

Question 20

A scientist wants to find the z-score that separates the lowest $$10\% of $$data from the rest in a standard normal distribution. What is the z-score?

Accepted Answer

$$z = -1.28$$

Standard Normal Distribution: Calculating Probabilities and Z-Scores Using the TI-84 Calculator

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