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Use the normal distribution of SAT critical reading scores for which the mean is 506 and...

Use the normal distribution of SAT critical reading scores for which the mean is

506 and the standard deviation is 110.

Assume the variable x is normally distributed.

(a)

What percent of the SAT verbal scores are less than

650​?

(b)

If 1000 SAT verbal scores are randomly​ selected, about how many would you expect to be greater than

575​?
math   Statistics-And-Probability   
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Answer #1

Mean = mu = 506

Standard deviation = sigma = 110

a) What percent of the SAT verbal scores are less than 650​ ?

X = 650

Z scores = ( X - mu ) / sigma

= (650 - 506)/110

= 1.3090

P( Z < 1.3090 ) = 0.9047

= 90.47% (Z- chart refer below screenshot)

.3 -1 Area from a value (Use to compute p from Z) Value from an area (Use to compute Z for confidence intervals) Specify Parameters Mean 0 SD 1 Above Below 1.3090 Between Outside and and Results: Area (probability) 0.9047000000 Recalculate

b) If 1000 SAT verbal scores are randomly​ selected, about how many would you expect to be greater than

575​?

Z = (575 - 506 )/ 110

= 0.6272

P( Z > 575 ) = 0.2653 = 26.53%

26.53% of 1000

= 265.3

265 scores

.3 -2 -1 Area from a value (Use to compute p from Z) O Value from an area (Use to compute Z for confidence intervals) Specify Parameters: Mean 0 SD 1 Above 0.6272 Below Between Outside and an Results: Area (probability) 0.2653 Recalculate

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Answer #2

P(z<0.73)

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