Probability of being under a number

[granite]

The average height of a male is 62 inches with a standard deviation of 5. In a sample of 12, what is the probability that half the adults will be less than 62 inches tall?

[brianlange77]

The average height of a male is 62 inches with a standard deviation of 5. In a sample of 12, what is the probability that half the adults will be less than 62 inches tall?

Granite:

Is this a question from a standard GMAT source? If so, can you also post the multiple choice answers associated with this?

Thanks.

-Brian

[Brent@GMATPrepNow]

The average height of a male is 62 inches with a standard deviation of 5. In a sample of 12, what is the probability that half the adults will be less than 62 inches tall?

As it stands, this question could have several different answers.
If we have a sample of 12 men, then to find the probability that six of them are less than 62 inches tall, we need to know the probability that one randomly-selected male is less than 62 inches tall. In other word, what fraction of the entire male population is less than 62 inches?

Knowing that average height of a male is 62 inches with a standard deviation of 5 doesn't help us here, because it still doesn't provide us with the key piece of information: the probability that one randomly-selected male is less than 62 inches tall.

Now, if the heights of men were normally distributed, then we might conclude that half the men are more than 62 inches tall, and half are less than 62 inches tall, in which case we could answer the question.

Having said that, the concept of normal distributions is not tested on the GMAT.

Cheers,
Brent