A toy consists of three parts whose respective weights (measured in grams are de

Question

A toy consists of three parts whose respective weights (measured in grams are denoted X_1, X_2, X_3. Assume that the weights are independent and normally distributed with x_1^- = 150, sigma_1^2 = 36, x_2^- = 100, sigma_2^2 = 25, x_3^- = 250, sigma_3^2 = 60 a) What proportion of the toys have weight greater than 520 g? b) Suppose the toys are shipped 24 to box. The box, itself, weighs 200 g. Calculate the expected value and variance of the total weight of the box and its contents. c) Calculate the probability that the total weight of the box and its contents is greater than 12, 300 g.

Explanation / Answer

Answer:

a).

weight of toy = 150+100+250=500

variance of toy =36+25+60=121

sd= sqrt(121) =11

z value for 520, z =(520-500)/11=1.82

P( x>520) = P( z>1.82)

=0.0344

b).

expected value of box 200+24*500=12200

Variance of the box = 24^2*121 =69696

c).

Sd of the box=264

Z value for 12300, z =(12300-12200)/264 =

=0.38

P( x >12300) = P(z >0.38)

=0.352

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