The College Board originally scaled SAT scores so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100. Assuming scores follow a bell-shaped distribution, use the empirical rule to find the percentage of students who scored less than 400. a. 84% b. 16%

b. 16%

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 500

Standard deviation = 100

Percentage of students who scored less than 400:

400 = 500 - 1*100

So 400 is one standard deviation below the mean.

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

Of those who are below, 68% are within 1 standard deviation of the mean, that is, between 400 and 500. So 100-68 = 32% are below 400.

0.5*0.32 = 0.16 = 16%

So the correct answer is:

b. 16%

step-by-step explanation:

10.50 + taxes which added up to 11.50

solution:

as, mean is defined as sum of all the observations divided by total number of observations.

and , median is mid value of the data whether arranged in ascending order or descending order.

consider, roadsters:

2,3,4,5,6,7,8,9

mean =

also, median= , because number of observations is even, so median is mean of two mid values.

now, coming to bandits

2,3,4,5,6

mean =  

median = 4, as number of observations is odd.

so, roadsters has greater median as well mean than bandits.

→option a is true about the repairs performed on 2 types of cars:

bandits have lower median and mean than roadsters.