Question

A process X is a normally distributed population with mean = 14 and variance 16. Determine the probability that 14 objects selected will have mean is greater than 15.2.

Answer 1

Here's how to approach this problem.  First write down the given variables as stated in the problem.

• Mean = 14
• Variance = 16

Now, recall that Standard deviation (sd) = √ variance

Substitute the values we were given in the problem;

sd = √ 16 = 4

With the help of the standard normal distribution table;

P(X > 15.2) = P ( Z > (15.2 - 14) / 4 )

= P(Z > 0.3)

= 1 - 0.6179

= 0.3821

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