Given that z is a standard normal random variable, compute the following P(0 < z < .92)Question 7Select one:a.0.2182b.0.8212c.0.5912d.0.3212
Question
Given that z is a standard normal random variable, compute the following P(0 < z < .92)Question 7Select one:a.0.2182b.0.8212c.0.5912d.0.3212
Solution
To solve this problem, we need to use the standard normal distribution table or Z-table. The Z-table gives us the probability that a standard normal random variable Z is less than a given value z.
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First, we need to find the probability P(Z < 0.92). Looking up 0.92 in the Z-table, we find that the probability is approximately 0.8212.
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Next, we need to find the probability P(Z < 0). Since Z is a standard normal random variable, it has a mean of 0. Therefore, P(Z < 0) is 0.5.
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To find P(0 < Z < 0.92), we subtract P(Z < 0) from P(Z < 0.92). So, P(0 < Z < 0.92) = P(Z < 0.92) - P(Z < 0) = 0.8212 - 0.5 = 0.3212.
So, the answer is d. 0.3212.
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