Question

A company makes Citi bikes. 95% (i.e., 0.95) pass final inspection. Suppose that 5 bikes are randomly selected. ( use binomial distribution formula )a)What is the probability that exactly 4 of these 5 sports bikes pass final inspection?b)What is the probability that less than 3 of these 5 sports bikes pass final inspection? ()Do I use the factorial symbol that looks like an! When do you do Step by Step when solving problem I got disconnected from my last two digits of my Wi-Fi please help ASAP this is speaking a foreign language to me What is supposed to show step by step by hand

Answer 1

Given:

`\begin{gathered} p=0.95 \\ q=1-0.95=0.05 \\ n=5 \end{gathered}`

Using the binomial distribution formula;

`P(x)=^nC_xp^xq^(n-x)`

a) Probability that exactly 4 pass the final inspection.

`\begin{gathered} P(4)=^5C_4*0.95^4*0.05^(5-4) \\ P(4)=0.2036265625 \end{gathered}`

b) Probability that less than 3 pass.

`P(<3)=P(2)+P(1)+P(0)`

Hence,

`\begin{gathered} P(2)=^5C_2*0.95^2*0.05^(5-2) \\ P(2)=0.001128125 \end{gathered}`
`\begin{gathered} P(1)=^5C_1*0.95^1*0.05^(5-1) \\ P(1)=0.0000296875 \end{gathered}`
`\begin{gathered} P(0)=^5C_0*0.95^0*0.05^(5-0) \\ P(0)=0.0000003125 \end{gathered}`

Thus,

`\begin{gathered} P(<3)=P(2)+P(1)+P(0) \\ P(<3)=0.001128125+0.0000296875+0.0000003125 \\ P(<3)=0.001158125 \end{gathered}`