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Z is a standard normal random variable. Compute the probabilities. P(-1.33 ≤ z ≤ 1.67)

User Taruna
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Final answer:

To compute P(-1.33 ≤ z ≤ 1.67), find the area to the left of z = 1.67 (A2) and subtract from it the area to the left of z = -1.33 (A1) using a z-table or calculator. The result is the probability of z falling between the given values.

Step-by-step explanation:

To compute the probability that a standard normal random variable, Z, falls between -1.33 and 1.67, we need to find the area under the standard normal curve between these z-scores. This requires looking up each z-score in a z-table or using a calculator. Once we find the area to the left of z = 1.67 and subtract the area to the left of z = -1.33 from it, we will have our probability.

The z-table usually gives the area to the left of the z-score. For z = -1.33, assume we have looked it up and found the area is A1. For z = 1.67, let's call the area A2. So, the probability P(-1.33 ≤ z ≤ 1.67) is A2 - A1.

If a z-table is not available, one can use a calculator with statistical functions, such as the TI-83, or any calculator that provides the invNorm function. You would calculate the areas by entering the z-scores as arguments into this function. Additionally, you can use software or online tools that provide a standard normal distribution calculator.

User Payal Maniyar
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