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1 vote
Assume Z is a standard normal random variable. Then P(-1.20 sz s 1.50) equals

a. .3849
b..0483
C..8181
d. 4332

User Deepu T
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1 Answer

2 votes

Final Answer:

The probability P(-1.20 sz s 1.50) equals 0.8181, thus the correct option is C.

Explanation:

Z is a standard normal random variable, which has a mean of 0 and a standard deviation of 1. To calculate the probability of P(-1.20 sz s 1.50), we can use the z-score table to look up the area to the left of 1.50 and subtract the area to the left of -1.20. The area to the left of -1.20 is 0.0953, and the area to the left of 1.50 is 0.9334. Subtracting the area to the left of -1.20 from the area to the left of 1.50 gives 0.8181, which is the probability of P(-1.20 sz s 1.50).

To calculate this probability in another way, we can use the formula for the z-score, which is z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation. Since Z is a standard normal random variable, the mean and standard deviation are 0 and 1, respectively. Using this formula for the two given values, -1.20 and 1.50, we get the z-scores of -1.20 and 1.50, respectively.

Using the z-score table, we look up the area to the left of 1.50 and subtract the area to the left of -1.20. The area to the left of -1.20 is 0.0953, and the area to the left of 1.50 is 0.9334. Subtracting the area to the left of -1.20 from the area to the left of 1.50 gives 0.8181, which is the probability of P(-1.20 sz s 1.50).

Therefore, the probability P(-1.20 sz s 1.50) equals 0.8181.

User Aerobiomat
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