In a recent year, scores on a standardized test for high school students with a

Question

In a recent year, scores on a standardized test for high school students with a 3.50 to 4.00 grade point average were normally distributed, with a mean of 37.9 and a standard deviation of 1.6. A student with a 3.50 to 4.00 grade point average who took the standardized test is randomly selected.

The probability of a student scoring less than35 is nothing.

(Round to four decimal places as needed.)

(b) Find the probability that the student's test score is between

35.5 and 40.3

The probability of a student scoring between

35.5 and 40.3is nothing.

(Round to four decimal places as needed.)

(c) Find the probability that the student's test score is more than

39.1

The probability of a student scoring more than

39.

is

nothing.

(Round to four decimal places as needed.)

Explanation / Answer

a)For X=35, z=(x-mu)/sigma=(35-37.9)/1.6=-1.81

P(X<35)=P(z<-1.81)=0.0351

b)For X=35.5, z=(35.5-37.9)/1.6=-1.5

For X=40.3, z=(40.3-37.9)/1.6=1.5

P(35.5<X<40.3)=P(X<40.3)-P(X<35.5)

=P(z<1.5)-P(z<-1.5)

=0.9332-0.0668=0.8664

c)For X=39.1, z=(39.1-37.9)/1.6=0.75

P(X>39.1)=P(z>0.75)=1-P(z<0.75)

=1-0.7734

=0.2266

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