Question

I NEED HELP ASAP , no tutor was able to solve this.

Answer 1

given

Number of customers = 20

number of successes = 30% = 0.30

Find

a) Probability of exactly 15 customers will make a purchase.

b) Probability of atleast 15 customers will make a purchase.

c) Probability of atmost 4 customers will make a purchase.

Explanation

here we use binomial distribution.

n = 20

p = 0.30

q = 1 - 0.30 = 0.70

a) Probability of exactly 15 customers will make a purchase =

$\begin{gathered} ^{20}C_{15}(0.30)^{15}(0.70)^5 \\ \frac{20!}{5!15!}(0.30)^{15}(0.70)^5 \\ \frac{20\times19\times18\times17\times16}{5\times4\times3\times2\times1}\times(0.30)^{15}(0.70)^5 \\ 0.00004 \\ \end{gathered}$

b) Probability of atleast 15 customers will make a purchase =

$\begin{gathered} P(X\ge15)=0.00005 \\ \end{gathered}$

c) Probability of atmost 4 customers will make a purchase =

$P(X\leq4)=0.23751$

Final Answer

Hence

a) 0.00004

b) 0.00005

c) 0.2375