Question

X is a normally distributed random variable with mean 57 and standard deviation 19.

What is the probability that X is between 38 and 76?
SALLE
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Write your answer as a decimal rounded to the nearest thousandth.​

Answer 1

To find the probability that X is between 38 and 76, we can calculate the z-scores for these values and use a standard normal distribution table or calculator.

Step-by-step explanation:

To find the probability that X is between 38 and 76, we need to find the area under the normal curve between these values. We can use the standard normal distribution and convert the values to z-scores.

The z-score for 38 is calculated as: z = (38 - 57) / 19 = -0.947.
The z-score for 76 is calculated as: z = (76 - 57) / 19 = 1.

Using a standard normal distribution table or a calculator, we can find the proportion of values between these two z-scores. The probability that X is between 38 and 76 is approximately 0.684.