Question

Please enter this homework question in round your answer to at least three decimal places do not round any intermediate steps thanks

Answer 1

ANSWER:

0.195

STEP-BY-STEP EXPLANATION:

Given:

p = 58% = 0.58

Sample size (n) = 50

We can calculate the mean and standard deviation as follows:

$\begin{gathered} \mu=np=50\cdot0.58 \\ \\ \mu=29 \\ \\ \sigma=\sqrt{n\cdot p\cdot(1-p)}=\sqrt{50\cdot0.58\cdot(1-0.58)} \\ \\ \sigma=3.49 \\ \end{gathered}$

Now we must calculate the probability of at least 32, therefore:

$\begin{gathered} P(x\ge32)=1-P(x\leq32) \\ \\ P(x\leq32)=P\left(\frac{x-\mu}{\sigma}\le\frac{32-29}{3.49}\right) \\ \\ (x\leq32)=P\left(z\le0.86\right) \end{gathered}$

We use the normal table to determine the probability, like this:

$\begin{gathered} P(x\ge32)=1-0.8051 \\ \\ P(x\ge32)=0.1949\approx0.195 \end{gathered}$

Therefore, the correct answer is 0.195