Question

Which of the following probabilities is the greatest for a standard normal distribution? P (negative 1.5 less-than-or-equal-to z less-than-or-equal-to negative 0.5) P (negative 0.5 less-than-or-equal-to z less-than-or-equal-to 0.5) P (0.5 less-than-or-equal-to z less-than-or-equal-to 1.5) P (1.5 less-than-or-equal-to z less-than-or-equal-to 2.5)

Answer 1

The probability P(-0.5 ≤ z ≤ 0.5) is the greatest for a standard normal distribution, and the value of P(-0.5 ≤ z ≤ 0.5) is 38.2% option second is correct.

What is a normal distribution?

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have a statement:

Which of the following probabilities is the greatest for a standard normal distribution:

The options are:

P(-1.5 ≤ z ≤ -0.5)

P(-0.5 ≤ z ≤ 0.5)

P(0.5 ≤ z ≤ 1.5)

P(1.5 ≤ z ≤ 2.5)

As we know from the normal distribution curve we can find the probability between the range given. At Z=0, the chance is 50-50.

From the Z-curve:

P(-1.5 ≤ z ≤ -0.5)  = 9.2% + 15% = 24.2%

P(-0.5 ≤ z ≤ 0.5) = 19.1% + 19.1% = 38.2%

P(0.5 ≤ z ≤ 1.5) = 15% + 9.2% = 24.2%

P(1.5 ≤ z ≤ 2.5) = 4.4% + 1.7% = 6.1%

Thus, the probability P(-0.5 ≤ z ≤ 0.5) is the greatest for a standard normal distribution, and the value of P(-0.5 ≤ z ≤ 0.5) is 38.2% option second is correct.

Learn more about the normal distribution here:

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