Question

EJERCICIO DE ESTADISTICAThe proportion of individuals insured by the All-Driver Automobile Insurance Company who received at least one traffic ticket during a five-year period is .15.a. Show the sampling distribution of if a random sample of 150 insured individuals is used to estimate the proportion having received at least one ticket.b. What is the probability that the sample proportion will be within ±.03 of the population proportion?

Answer 1

Given that;

The proportion of individuals insured by the All-Driver Automobile Insurance Company who received at least one traffic ticket during a five-year period is .15

That is,

`\mu=0.15`

If a random sample of 150 insured individuals is used to estimate the proportion having received at least one ticket, the formula to show the sampling proportion is

`\begin{gathered} \sigma=\sqrt{(\mu(1-\mu))/(n)} \\ \sigma=\sqrt{(0.15(1-0.15))/(150)}=0.0292 \end{gathered}`

Hence, the answer is 0.0292 (four decimal places)

It is approximately normal.

b)

`\begin{gathered} (0.03)/(0.0292)=1.0290 \\ (-0.03)/(0.0292)=-1.0290 \end{gathered}`

The probability the sample proportion will be

`2P\left(0\leq z\leq1.0292\right)=0.6966`

Hence, the answer is 0.6966 (four decimal places)