Job Trends Analysis: Normal Approximation & Z-Values

Step 1 of 4

(a)

We have given a random sample of 150 people who are employed.

According to the government, 5.3% of those employed have arc multiple-job holders.

We are asked the probability that fewer than 10 hold multiple jobs.

Let \(x\) denote the number of people who hold multiple jobs.

We need to find \(P(X<10)\).

Here we will use the normal approximation to the binomial approximation.

Here, \(p=5.3 \%=0.053, q=0.947\), and \(n=150\).

Check to see whether a normal approximation can be used.

\(n p=0.053 \times 150=7.95, a n d n q=150 \times 0.947=142.05\)

Since \(n p \geq 5\) and \(n q \geq 5\), the normal distribution can be used.

Find the mean and standard deviation.

\(\text { mean }=\mu=n p=0.053 \times 150=7.95\)

\(\text { standard deviation }=\sigma=\sqrt{n p q}=\sqrt{150 \times 0.947 \times 0.053}=2.744\)