The probability P(-2 ≤ Z ≤ 2) for a standard normal distribution can be found using the standard normal distribution table or using a calculator with a normal distribution function.

Here are the steps to calculate it:

1. Identify the given values. In this case, the lower limit of the range is -2 and the upper limit is 2.

2. Look up the Z-scores in the standard normal distribution table. The value you find is the probability that Z is less than or equal to that Z-score. For Z = 2, the value is approximately 0.9772. For Z = -2, the value is approximately 0.0228.

3. Since the standard normal distribution is symmetric around 0, P(Z ≤ 2) = P(Z ≥ -2). Therefore, P(-2 ≤ Z ≤ 2) = P(Z ≤ 2) - P(Z ≤ -2) = 0.9772 - 0.0228 = 0.9544.

So, the probability that a standard normal random variable Z falls between -2 and 2 is approximately 0.9544 or 95.44%.

Question

The probability P(-2 ≤ Z ≤ 2) for a standard normal distribution can be found using the standard normal distribution table or using a calculator with a normal distribution function.

Here are the steps to calculate it:

1. Identify the given values. In this case, the lower limit of the range is -2 and the upper limit is 2.

2. Look up the Z-scores in the standard normal distribution table. The value you find is the probability that Z is less than or equal to that Z-score. For Z = 2, the value is approximately 0.9772. For Z = -2, the value is approximately 0.0228.

3. Since the standard normal distribution is symmetric around 0, P(Z ≤ 2) = P(Z ≥ -2). Therefore, P(-2 ≤ Z ≤ 2) = P(Z ≤ 2) - P(Z ≤ -2) = 0.9772 - 0.0228 = 0.9544.

So, the probability that a standard normal random variable Z falls between -2 and 2 is approximately 0.9544 or 95.44%.

Knowee AI · Accepted Answer

The probability P(-2 ≤ Z ≤ 2) for a standard normal distribution can be found using the standard normal distribution table or using a calculator with a normal distribution function.

Here are the steps to calculate it:

1. Identify the given values. In this case, the lower limit of the range is -2 and the upper limit is 2.

2. Look up the Z-scores in the standard normal distribution table. The value you find is the probability that Z is less than or equal to that Z-score. For Z = 2, the value is approximately 0.9772. For Z = -2, the value is approximately 0.0228.

3. Since the standard normal distribution is symmetric around 0, P(Z ≤ 2) = P(Z ≥ -2). Therefore, P(-2 ≤ Z ≤ 2) = P(Z ≤ 2) - P(Z ≤ -2) = 0.9772 - 0.0228 = 0.9544.

So, the probability that a standard normal random variable Z falls between -2 and 2 is approximately 0.9544 or 95.44%.

Let Z be a standard normal random variable. Calculate P (−2 Z 2)?

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