PROBABILITY and STATISTICS

Question

A population of values has a normal distribution with �=226.5 and �=62.7. You intend to draw a random sample of size �=80.

Answer the following, rounding your answers to three decimals where appropriate.

Find the probability that a single randomly selected value is less than 231.4.

P(X < 231.4) = 

Answer 1

You can either use a calculator or tables. Here is the calculator answer with the following parameters:

µ = 226.5

σ = 62.7

N = 80

P(x<231.4) ≈ 0.757722

to 6 decimal places, or 0.758 to 3 decimal places.

To use the tables, first calculate the z-score:

(231.4-226.5) / (62.7 / √80) ≈ 0.6989941365

Then use this value in the tables.