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Find the indicated probability for the standard normal Z: P(1.35< Z < 1.72)

Question

Find the indicated probability for the standard normal Z: P(1.35< Z < 1.72)

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Solution

To find the probability that a standard normal random variable Z is between 1.35 and 1.72, you need to use the standard normal distribution table or a calculator with a normal distribution function.

Here are the steps:

  1. Look up the Z-score for 1.35 in the standard normal distribution table. The value you get is the probability that Z is less than 1.35. Let's call this value P1.

  2. Look up the Z-score for 1.72 in the same table. The value you get is the probability that Z is less than 1.72. Let's call this value P2.

  3. Subtract P1 from P2 to get the probability that Z is between 1.35 and 1.72. In other words, P(1.35< Z < 1.72) = P2 - P1.

Remember that the values you get from the table are cumulative probabilities, so when you subtract P1 from P2, you're finding the probability of Z falling in that specific range.

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