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Compute probabilities.
The area under the normal curve from x = a to x = b with given mean and standard deviation is the probability that x assumes a value between x = a and x = b. If we are using Table IV in Appendix C, we need to standardize the random variable x using the formula z = (x - µ)/σ, before using the table.
where µ is the mean and σ is the standard deviation of the normal distribution. We use 1E99 for ∞ and -1E99 for -∞, if needed.
Let x be a continuous random variable that is normally distributed with a mean of 24 and a standard deviation of 7.
Round your answers to two decimal places.
(a) Standardize the variable value x = 27.5.
z =
(b) Standardize the variable value x = 59.0.
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