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.