Question

Use the normal distribution of SAT critical reading scores for which the mean is 506 and the standard deviation is 125.

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 525​?

Answer 1

Solution :

Given that ,

mean = = 506

standard deviation = =    125

a]

P(X< 650) = P[(X- ) / < (650-506) / 125]

= P(z <1.15 )

Using z table

= 0.8749

answer=87.49%

b]   Solution :

Given ,

mean = = 506

standard deviation = = 125

n=1000

P(x >525 ) = 1 - P(x<525 )

= 1 - P[(x -) / < (525-506) / 125]

= 1 - P(z <0.15 )

Using z table

= 1 - 0.5596

= 0.4404*1000

=440.4

answer=440