Question

Calculate the probability for P(z>2.48)

Answer 1

The probability that a standard normal random variable \(z\) is greater than 2.48 is approximately 0.0067.

To calculate the probability \(P(z > 2.48)\), where \(z\) is a standard normal random variable, you can use a standard normal distribution table or a calculator.

1. Refer to a standard normal distribution table or use a calculator with a normal distribution function.

2. Look up the z-score of 2.48 in the table or calculate it using the formula:
`\[z = (x - \mu)/(\sigma),\]` where \(x\) is the value,
`\(\mu\)` is the mean (which is 0 for the standard normal distribution), and
`\(\sigma\)` is the standard deviation (which is 1 for the standard normal distribution).

3. Once you find the z-score, look up the corresponding probability in the table or use the calculator.

4. The probability
`\(P(z > 2.48)\)` is the area under the standard normal curve to the right of the z-score.

5. In this case,
`\(P(z > 2.48) \approx 0.0067\)`.

Therefore, the probability that a standard normal random variable \(z\) is greater than 2.48 is approximately 0.0067.