Question

the results of a certain medical test are normally distributed with a mean of 125 and a standard deviation of 19. convert the given results into z - scores, and then use the accompanying table of z - scores and percentiles to find the percentage of people with readings between 120 and 130. click the icon to view the table of z - scores and percentiles. the percentage of people with readings between 120 and 130 is % (round to two decimal places as needed.)

Explanation:

Step1: Calculate the z - score for \(x = 120\)

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 125\) (mean) and \(\sigma=19\) (standard deviation).
For \(x = 120\), \(z_1=\frac{120 - 125}{19}=\frac{-5}{19}\approx - 0.26\)

Step2: Calculate the z - score for \(x = 130\)

For \(x = 130\), \(z_2=\frac{130 - 125}{19}=\frac{5}{19}\approx0.26\)

Step3: Find the percentage using the z - score table

The percentage of data to the left of \(z=-0.26\) is \(0.3974\) (from the standard normal table).
The percentage of data to the left of \(z = 0.26\) is \(0.6026\) (from the standard normal table).
The percentage of data between \(z=-0.26\) and \(z = 0.26\) is \(P(-0.26<Z<0.26)=0.6026 - 0.3974\)

Answer:

\(20.52\%\)