Question

The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean of 320 and population standard deviation of 20 inches. For a randomly chosen Monday, what is the probability there will be between 280 and 360 column inches of classified advertisement?

Answer 1

Answer:

The probability there will be between 280 and 360 column inches of classified advertisement

P(280≤X≤360) = P(-2≤Z≤2) = 0.9544

Step-by-step explanation:

Step(i):-

Given that the mean  the population = 320

The standard deviation of the Population = 20

Let 'X' be the random variable in a normal distribution

Let 'X' = 280

$Z = \frac{x-mean}{S.D} = \frac{280-320}{20} = -2$

Let 'X' = 360

$Z = \frac{x-mean}{S.D} = \frac{360-320}{20} = 2$

Step(iii):-

The probability there will be between 280 and 360 column inches of classified advertisement

P(280≤X≤360) = P(-2≤Z≤2)

                        = P(z≤2) -P(z≤-2)

                       = P(z≤2)+P(z≤2)

                      = 2P(z≤2)

                     = 2×0.4772     ( from normal table)

                    = 0.9544