Answer:
Correct option is (d): Neither X nor Y can be well-approximated by a normal random variable.
Step-by-step explanation:
The sample size of males having color-blindness is, n (X) = 20.
The sample size of females having color-blindness is, n (Y) = 40.
The proportion of males that suffer from color-blindness is, P (X) = 0.08.
The proportion of females that suffer from color-blindness is, P (Y) = 0.01.
Now both the random variables <em>X</em> and <em>Y</em> follows a Binomial distribution,
A normal distribution is used to approximate the binomial distribution if the sample is large, i.e <em>n</em> ≥ 30 and the probability of success is very close to 0.50.
Also if <em>np</em> ≥ 10 and <em>n</em> (1 - <em>p</em>) ≥ 10, the binomial distribution can be approximated by the normal distribution.
<u>For the sample of men (X):</u>
In this case neither <em>n</em> > 30 nor <em>p</em> is close to 0.50.
And <em>np</em> < 10.
Thus, the random variable <em>X</em> cannot be approximated by the normal distribution.
<u>For the sample of men (Y):</u>
In this case <em>n</em> > 30 but <em>p</em> is not close to 0.50.
And <em>np</em> < 10.
Thus, the random variable <em>Y</em> cannot be approximated by the normal distribution.
Thus, both the random variables cannot be approximated by the normal distribution.
The correct option is (d).