Question

33. 2017 SAT scores All sections of the test are known to be normally distributed with mean of approximately mean of 1060 and standard deviation of 195

(a) Draw a normal curve with the parameters labeled.

(b) Shade the region that represents the proportion of test takers who scored less than 1200.

(c) Suppose the area under the normal curve to the left of X = 1200 is 0.7636. Provide two interpretations of this result.

Answer 1

SOLUTION:

From given data,

2017 SAT scores All sections of the test are known to be normally distributed with mean of approximately mean of 1060 and standard deviation of 195

where,

Mean = = 1060

Standard deviation = = 195

(a) Draw a normal curve with the parameters labeled.

(b) Shade the region that represents the proportion of test takers who scored less than 1200.

where,

P[X<1200] = P[X- / < 1200-1060 / 195]

= P[Z < 1200-1060 / 195]

= P[Z < 140 / 195]

   = P[Z < 0.72]

= 0.7642

(c) Suppose the area under the normal curve to the left of X = 1200 is 0.7636. Provide two interpretations of this result.

Now, in the above curve ,

when area under the normal curve to the left of 1200 is 0.7636 it means,

(a) 1200 is 1 standard deviation above the mean.

(b) 1200 covers 76% of area below it and 24% of area above 1200 .

area below x=1200 is shown in the standard region.