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.

Step-by-step 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 \\ (20!)/(5!15!)(0.30)^(15)(0.70)^5 \\ (20*19*18*17*16)/(5*4*3*2*1)*(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