"quantity"exercise:standardized random variable
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Questions 1:
The following is an excerpt from the cumulative distribution function for the standard normal random variable table:
A variable is normally distributed with a mean of 2.00 and a variance of 16.00. Using the excerpt, the probability of observing a value of 7.40 or less is closest to:
A 、63.3%.
B 、91.2%.
C、 96.8%.
Questions 2:
Which of the following most accurately describes how to standardize a random variable X?
A 、Subtract the mean of X from X, and then divide that result by the standard deviation of the standard normal distribution.
B 、Divide X by the difference between the standard deviation of X and the standard deviation of the standard normal distribution.
C、Subtract the mean of X from X, and then divide that result by the standard deviation of X.
B is correct. First the outcome of interest, 7.40, is standardized for the given normal distribution:
Then, the given table of values is used to find the probability of a Z-value being less than or equal to 1.35 standard deviations above the mean. The value is P(Z ≤ 1.35) = 0.9115 = 91.2%
A is incorrect; it divides 5.4 (that is the result of 7.4 – 2) by the variance, 16, and uses 0.34 as the z-value: P(Z≤0.34) = 0.6331 = 63.3%.
C is incorrect; it divides the value, 7.4, by the standard deviation, 4, and uses 1.85 as the Z-value: P(Z ≤ 1.85) = 0.9678 = 96.8%.
C is correct. There are two steps in standardizing a random variable X: Subtract the mean of X from X, and then divide that result by the standard deviation of X. This is represented by the following formula: Z = (X – μ)/σ.
A is incorrect. There are two steps in standardizing a random variable X: Subtract the mean of X from X, and then divide that result by the standard deviation of X. This is represented by the following formula: Z = (X – μ)/σ.
B is incorrect. There are two steps in standardizing a random variable X: Subtract the mean of X from X, and then divide that result by the standard deviation of X. This is represented by the following formula: Z = (X – μ)/σ
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