Question

c) ( p(\bar{x} geq 63.3)= ) (round to four decimal places as needed.) b) ( p(\bar{x}<65.7)=0.7746 ) (round to four decimal places as needed.) c. normal, with ( mu_{\bar{x}}=62 ) and ( sigma_{\bar{x}}=19 )

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\). Here, \(\mu = 62\), \(\sigma=19\), and \(x = 63.3\).

$$z=\frac{63.3 - 62}{19}=\frac{1.3}{19}\approx0.07$$

Step2: Find the probability using the standard normal table

We want to find \(P(X\geq63.3)\), which is equivalent to \(1 - P(X < 63.3)\).
Looking up the z - score \(z = 0.07\) in the standard normal table, \(P(Z<0.07)=0.5279\)

$$P(X\geq63.3)=1 - 0.5279=0.4721$$

Answer:

\(0.4721\)