Answer:
The probability of X < 15 is 0.054.
Step-by-step explanation:
The random variable X is defined as the number of neutrophils.
The number of white blood cells sampled is, n = 50.
The proportion of neutrophils is, p = 0.40.
A randomly sampled white blood cells is a neutrophil or not is independent of all the other white blood cells.
The random variable X thus follows a Binomial distribution with parameters n = 50 and p = 0.40.
The probability mass function of the Binomial distribution is:
[tex]P(X=x)={n\choose x}\ p^{x}\ (1-p)^{n-x};\ x=0,1,2,3...[/tex]
Compute the probability of X < 15 as follows:
[tex]P (X < 15) =1- P (X \geq 15)[/tex]
[tex]=1-[\sum\limits^{15}_{i=0}{{50\choose x}\ (0.40)^{x}\ (1-0.40)^{50-x}}]\\\\=1-[0+0+...+0.04155]\\\\=1-0.94604\\\\=0.05396\\\\\approx 0.054[/tex]
Thus, the probability of X < 15 is 0.054.
