A certain standardized test's math scores have a bell-shaped distribution with a mean of 520 and a standard deviation of 110. Complete parts (a) through (c). (a) What percentage of standardized test scores is between 190 and 850? ____ (Round to one decimal place as needed.) (b) What percentage of standardized test scores is less than 190 or greater than 850? ____ (Round to one decimal place as needed.)(c) What percentage of standardized test scores is greater than 740? ____ (Round to one decimal place as needed.)
Accepted Solution
A:
Answer:(a) 99.7%(b) 0.3%(c) 2.5%Step-by-step explanation:This problem doesnt require a z-table as long as you know the basic rule of 68, 95 and 99.7.If you are +-1 standard deviation from the mean the percentage in that band correspond to the 68% of the values.If you are +-2 standard deviation from the mean the percentage in that band correspond to the 95% of the values.If you are +-3 standard deviation from the mean the percentage in that band correspond to the 99.7% of the values.The formula to calculate z-score is:[tex]z=\frac{x-\mu}{\sigma}[/tex][tex]x\ is \ the\ number\ evaluated\\\mu\ is\ the\ mean\\\sigma\ is \ the \standard\ deviation[/tex](a)lower z = (190 - 520)/110 = -3upper z = (850 - 520)/110 = 3This mean that you are looking for a percentage between +-3 standard deviation, exactly 99.7%(b)Since the percentage between is 99.7%, the percentage less than -3 standard deviation or greater than +3 standard deviation is 100 - 99.7 = 0.3%(c)z of 740 = (740 - 520)/110 = 2The percentage between +-2 is 95%, you are interested in the percentage greater than 2 and that is (100 - 95)/2 = 2.5%. You have to divide by 2 because 2.5% is less than -2 standard deviation and 2.5% is greater than 2 standard deviation, and you are only interested in the percetange greater than that