Lowe Lambert
09/13/2024 · High School

The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm and a standard deviation of 7.8 cm . a. Find the probability that an individual distance is greater than 207.50 cm . b. Find the probability that the mean for 25 randomly selected distances is greater than 196.20 cm . c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30 ?

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a. The probability that an individual distance is greater than 207.50 cm is approximately 0.0993 or 9.93%. b. The probability that the mean for 25 randomly selected distances is greater than 196.20 cm is approximately 0.7977 or 79.77%. c. The normal distribution can be used in part (b) because the population distribution is normally distributed, and the Central Limit Theorem allows us to use the normal distribution for the sample mean, regardless of the sample size.

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