Question

1. The grade of a Math Quiz is normally distributed with its mean, 81 and standard deviation, 8.4. If a student is randomly selected in class, what is the probability that his or her score will be higher than 90? 2. The historical data of a company's annual sales is normally distributed with its mean, $330 million and its standard deviation, $45 million. Find the probability that the company's sales will be between $300 million and $ 400 next year?

Answer 1

Solution : A der x = Grade of Math Quizz Given xx Noremal (M, c) where M = 81, 5=8.4 So, P( * >90) PCX-4 390.4) P(Z > 90-1) where Z= P(Z > 1.07) 1. P(Z $ 5.0+) xu ~ N(0,1) 1 -0.8577 [from Normai Dist" Area Table] - 0.1423 at det x= Annual sales of the company where Given xn Normal (4,0) M= So. P(900< x < 400) 330 millim o= $45 million. P ( 300-330 <X-4 < 400-330 45 45 o p(-0.67 LZ< 1.56 ) f(z< 4:56 )- (< - 0-6+) P(Z < 1.56 )-1 -1+ P(Z<0.67) 0.9406 - 1+ 0 1 + 0.7486 0.6892

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