Left-handedness occurs in about 12% of all americans. males are slightly more likely than females to be left-handed, with 13% of males and 11% of females being left-handed. suppose a random sample of 80 females and 100 males is chosen.

-let x be the number of males (out of the 100) who are left-handed.

-let y be the number of females (out of the 80) who are left-handed.

-let z be the total number of left-handed individuals in the sample (males and females together).

which of the following is true regarding the random variables x and y?

a)both x and y can be well approximated by normal random variables.
b)only x can be well approximated by a normal random variable.
c)only y can be well approximated by a normal random variable.
d)neither x nor y can be well approximated by a normal random variable.

a)Both X and Y can be well approximated by normal random variables.

Step-by-step explanation:

For each individual, there are only two possible outcomes. Either they are right-handed, or they are left-handed. This means that we can solve this problem using concepts of the binomial probability distribution.

Binomial probability:

Probability of exactly x sucesses on n repeated trials, with probability p.

The binomial probability can be well approximated by normal random variables, using the expected value and the standard deviation

Let X be the number of males (out of the 100) who are left-handed.

and . Can be well approximated.

Let Y be the number of females (out of the 80) who are left-handed.

and . Can be well approximated.

The correct answer is

a)Both X and Y can be well approximated by normal random variables.

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step-by-step explanation: