Probability and Statistics

Question

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

𝜇 = 28; 𝜎 = 3.8

P(x ≥ 30) =

Answer 1

Step 1: find the z score for x = 30

Z = (x-µ)/σ = (30-28)/3.8= .526

Z =.53 always round to the hundredths place since z scores are only given to 2 places in the standard table of normal distributions.

Step 2: find the area(probability) corresponding to the calculated z score

Now find z =.53 in that table. The area corresponding to z =.53 is .7019. This represents the area to the left of the z score.

Step 3 : Calculate the AREA ABOVE the z score

To obtain the area above the z score we must subtract from 1.

P(x≥30) = 1- .7019 = .2981

Therefore, your answer is .2981