2 Suppose that the weight of a paperback book is normally di

2. Suppose that the weight of a paperback book is normally distributed with mean mu = 8 ounces, and standard deviation sigma = 1.5 ounces. We can write X ~ N(8, 1.5). Answer the following questions: (a) if you randomly select a book, what is the probability that it weighs more than 11.5 ounces? (b) What is the probability of selecting a book that weighs between 10.3 and 14 ounces?

Solution

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    11.5      
u = mean =    8      
          
s = standard deviation =    1.5      
          
Thus,          
          
z = (x - u) / s =    2.333333333      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.333333333   ) =    0.009815329 [ANSWER]

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b)

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    10.3      
x2 = upper bound =    14      
u = mean =    8      
          
s = standard deviation =    1.5      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    1.533333333      
z2 = upper z score = (x2 - u) / s =    4      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.937403127      
P(z < z2) =    0.999968329      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.062565202   [ANSWER]