Left-handedness occurs in about 12% of all Americans. Males are slightly more li

Question

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? Both X and Y can be well approximated by normal random variables. Only X can be well approximated by a normal random variable. Only Y can be well approximated by a normal random variable. Neither X nor Y can be well approximated by a normal random variable.

Explanation / Answer

when np > 5 & n(1-p) = nq > 5

then X can be approximated using normal distribution

since every np & nq > 5 for both case

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

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