IMATH Hosted by ALEKS Corp Test. Ch 6, 7& 8 (8 ?s, 2 hrs in one sitting) Previou

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IMATH Hosted by ALEKS Corp Test. Ch 6, 7& 8 (8 ?s, 2 hrs in one sitting) Previous 12 3 45 6 78 Next Question 4 of 8 (1 point) View problem in a pop-up At a large publishing company, the mean age of proofreaders is 36.2 years and the standard deviation is 3.7 years. Assume the variable is normally distributed. Round intermediater-value calculations to two decimal places and the final answers to four decimal places. Part 1 out of 2 If a proofreader from the company is randomly selected, find the probability that his or her age will be between 36.5 and 38 years. P (36.5

Explanation / Answer

4.

NORMAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 36.2
standard Deviation ( sd )= 3.7

probability that his or her age will be between 36.5 and 38
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 36.5) = (36.5-36.2)/3.7
= 0.3/3.7 = 0.0811
= P ( Z <0.08) From Standard Normal Table
= 0.53
P(X < 38) = (38-36.2)/3.7
= 1.8/3.7 = 0.49
= P ( Z <0.49) From Standard Normal Table
= 0.69
P(36.5 < X < 38) = 0.69-0.53 = 0.15
=0.1500

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