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Part 1
In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 68.4 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts​ (a) through​ (d) below.
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Part 1
​(a) Find the probability that a study participant has a height that is less than 68 inches.
The probability that the study participant selected at random is less than 68 inches tall is

Sagot :

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Final answer:
The probability that the study participant selected at random is less than 68 inches tall is approximately 0.4602.

Explanation:
To find this probability, we use the z-score formula for a normal distribution. Given the mean height of 68.4 inches and a standard deviation of 4.0 inches, we calculate the z-score for 68 inches:
\[ z = \frac{68 - 68.4}{4.0} = -0.1 \]
Using a standard normal distribution table or calculator, the cumulative probability corresponding to a z-score of -0.1 is about 0.4602. Thus, the probability that a randomly selected participant is shorter than 68 inches is 0.4602, or 46.02%.
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