Question

suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data points between ( z = - 0.6 ) and ( z = 0.6 ) standard deviations of the mean (or within 0.6 standard deviations of the mean). what percent of the data points will fall in that range? answer: % round your percent to two decimal places and do not include the % sign in the answer box. check answer

Explanation:

Step1: Find the cumulative probability for \(z = 0.6\)

Using the standard normal distribution table (or a calculator with a normal - distribution function), the cumulative probability \(P(Z\leq0.6)\) is \(0.7257\).

Step2: Find the cumulative probability for \(z=-0.6\)

The cumulative probability \(P(Z\leq - 0.6)\) is \(0.2743\).

Step3: Calculate the probability between \(z=-0.6\) and \(z = 0.6\)

We use the formula \(P(-0.6<Z<0.6)=P(Z < 0.6)-P(Z<-0.6)\).
Substitute the values: \(P(-0.6 < Z < 0.6)=0.7257-0.2743 = 0.4514\).

Answer:

\(45.14\)