Question

Out of 1095people, what is the probability that exactly 2 were born on Jan.1 ? Assume 365days in a year

Short answer

The value of the function from binomial distribution is 0.224.

Step-by-step solution

Given Information

Number of people is $1095$

Definition of the Binomial distribution. 

Frequency distribution of the number of successful outcomes that can be achieved in a given number of trials, each with an equal chance of success.

Find the Binomial distribution.

The formula for binomial distribution states that.$f\left(x\right)=C(x,n)p^x{q}^{n-x}$

$\begin{array}{c}n=1095\\ p=\frac{1}{365}\\ x=2\end{array}$

Substitute the values mentioned above in the formula.

$\begin{array}{c}f\left(2\right)=C(1095,2){\left(\frac{1}{365}\right)}^2{\left(\frac{364}{365}\right)}^{1093}\\ =0.224\end{array}$

Find the corresponding normal approximation.

The formula for corresponding normal approximation states that .$f\left(x\right)=\frac{e^{-{(x-np)}^2/2npq}}{\sqrt{2\pi npq}}$

$\begin{array}{c}n=1095\\ p=\frac{1}{365}\\ x=2\end{array}$

Substitute the values mentioned above in the formula.

$\begin{array}{c}f\left(2\right)=\frac{e^{-3}\cdot 3^2}{2!}\\ =0.224\end{array}$

The value of the function from binomial distribution is .$0.224$