Question

population and the correction factor can be ignored. use the standard normal distribution table. round the final answers to four decimal places and intermediate = value calculations to two decimal places
part 1 of 3
find the probability that the mean of a sample of 25 people is less than 10.
p(\\( \overline { x } < 10 \\) ) = 0.0016
part 2 of 3
find the probability that the mean of a sample of 25 people is greater than 10.
p(\\( \overline { x } > 10 \\) ) =
part 3 of 3

Explanation:

Step1: Use the property of probability

We know that for any random variable \(X\), \(P(\overline{X}<a)+P(\overline{X}>a) = 1\) when \(a\) is a constant. Here \(a = 10\).

Step2: Substitute the known value

We are given that \(P(\overline{X}<10)=0.0016\). Then \(P(\overline{X}>10)=1 - P(\overline{X}<10)\)

Substitute \(P(\overline{X}<10) = 0.0016\) into the formula: \(P(\overline{X}>10)=1-0.0016\)

Step3: Calculate the result

\(1 - 0.0016=0.9984\)

Answer:

\(0.9984\)