Suppose there is a normally distributed population which has a mean of = 440 and

Question

Suppose there is a normally distributed population which has a mean of = 440 and a standard deviation of = 60. (5p) a. What z-score would correspond to a raw score of 260? b. What raw score would correspond to a z score of -3.5? c. If we randomly select one score from this population, what is the probability that will be less than 550? d. If we randomly select one score from this population, what is the probability that will be greater than 580? e. What portion of a normal distribution is below 295?

Explanation / Answer

we know that the z score is given as

z = (x-mean)/sd

please keep the z tables ready

a)

x = 260

we get z as
z = (260-440)/60 = -3

b)
again using the same formula

-3.5 = (x- 440)/60

x = 440 + 60*(-3.5) = 230

c)

again z = (550 - 440)/60 = 1.833
so p(z<1.833)
P ( Z<1.833 )=0.9664 (from the z table)

d)
p(x>580)

again z = (580 - 440)/60 = 2.33
P ( Z>2.33 )=1P ( Z<2.33 )=10.9901=0.0099

Please note that we can answer only 4 subparts of a question at a time , as per the answering guidelines

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