Assignment Use the empirical rule to draw conclusions about the data set below a

Question

Assignment Use the empirical rule to draw conclusions about the data set below and to determine the probability of Modules produced per week at Princess Foods Corporation. Production has been determined to be a normal distribution Average production is 5,000 Modules per week with a standard deviation of 200 Answer the following questions: 1. What is the probability that next week's production is between 4,800 and 5,400 2. What is the probability that next week's production be less than 4,400? 3. What is the probability that next week's production is between 5,200 and 5,600

Explanation / Answer

Here average production = 5000 modules per week

standard deviation = 200

(1) If x is the next week's production

Pr(4800 < x < 5400) = Pr(x < 5400; 5000 ; 200) - Pr(x < 4800 ; 5000 ; 200)

Z2 = (5400 - 5000)/200 = 2

Z1 = (4800 - 5000)/200 = -1

Pr(4800 < x < 5400) = Pr(x < 5400; 5000 ; 200) - Pr(x < 4800 ; 5000 ; 200) = Pr( Z < 2) - Pr(Z < -1)

= 0.977250 - 0.158655 = 0.8186

(2) Pr(x < 4400) = Pr(x < 4400 ; 5000 ; 200)

Z = (4400 - 5000)/200 = -3

Pr(x < 4400) = Pr(x < 4400 ; 5000 ; 200) = Pr(Z < -3) = 0.00135

(3) Pr(5200 < x < 5600) = Pr(x < 5600 ; 5000 ; 200) - Pr(x < 5200 ; 5000 ; 200)

Z2 = (5600 - 5000)/200 = 3

Z1 = (5200 - 5000)/200 = 1

Pr(5200 < x < 5600) = Pr(x < 5600 ; 5000 ; 200) - Pr(x < 5200 ; 5000 ; 200) = Pr(Z < 3) - Pr(Z < 1)

= 0.99865 - 0.841345

= 0.1573

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