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

Question

Use the normal distribution of SAT critical reading scores for which the mean is 504 and the standard deviation is 115. 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? (a) Approximately of the SAT verbal scores are less than 650 (Round to two decimal places as needed.) (b) You would expect that approximately SAT verbal scores would be greater than 575. (Round to the nearest whole number as needed.)

Explanation / Answer

A)
P(X<650)

I know that, z = (X-mean)/(sd)
z1 = (650-504)/115)
z1= 1.2696

hence,
P(X<650)
=P(Z<1.2696)
NORMSDIST(1.2696)
0.8979
89.79%

B)
P(X>575)
= 1-P(X<575)

I know that, z = (X-mean)/(sd)
z1 = (575-504)/115)
z1= 0.6174

hence,
P(X>575)
=1-P(Z<0.6174)
1-NORMSDIST(0.6174)
26.85%

Is thousand sat verbal scores are selected, then 26.85% of 1000 will be greater than 575.

In other words 268 individual score greater than 575 among 1000 selected individuals

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