Suppose x is a normally distributed random variable with muequals=1313 and sigma

mean = =13 standard deviation = =2 a) P(x 14.5) = 1-P(X

ID: 3208689 • Letter: S

Question

Suppose x is a normally distributed random variable with

muequals=1313

and

sigmaequals=22.

Find each of the following probabilities.a.

P(xgreater than or equals14.514.5)

P(xless than or equals9.59.5)

P(14.1414.14less than or equalsxless than or equals18.1218.12)

P(8.288.28less than or equalsxless than or equals16.4816.48)

Click here to view a table of areas under the standardized normal curve.

P(xgreater than or equals14.514.5)equals=nothing

(Round to three decimal places as needed.)

mean = =13

standard deviation = =2

P(x 14.5) = 1-P(X<14.5)

z value for 14.5 is (14.5-13)/2 = 1.5/2 = 0.75 ,p value = 0.773

P(X<14.5) =0.773

P(x 14.5) = 1- 0.773= 0.227

b)P(x<= 9.5)

z value for 9.5 is (9.5-13)/2 = -3.5/2 = -1.75 ,p value = 0.040059

P(x<= 9.5) = 0.040059

z value for 14.14 is (14.14-13)/2 = 1.14/2 = 0.57 ,p value = 0.715661

z value for 18.12 is (18.12-13)/2 = 5.12/2 = 2.56 ,p value = 0.987965

P(14.12<=x<= 18.12) =0.987965-0.715661 =0.2723

z value for 8.28 is (8.28-13)/2 = -3.72/2 = -0.186,p value = 0.426222

z value for 16.48 is (16.48-13)/2 = 3.48/2 =0.174 ,p value = 0.569067

P(8.28<=x<= 16.48) =0.569-0.426 =0.143

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