1 The number of pages in a population is normally distribute

1) The number of pages in a population is normally distributed with a mean of 38.2 pages and a standard deviation of 5.1 pages.

A. If a single report is randomly selected, find the probability that it is more than 50 pages long?

B. If a sample of 10 reports are randomly selected, find the probability that their mean length is more than 50 pages long. (Use your calculator)

2) 5% of the customers with reservations at a restaruant don\'t show up. Use a normal distribution to approximate the probability that at least 20 customers won\'t show up from a random group of 200 reservations. (Use your calcuator)

Solution

1.

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    50      
u = mean =    38.2      
          
s = standard deviation =    5.1      
          
Thus,          
          
z = (x - u) / s =    2.31372549      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.31372549   ) =    0.010341392 [ANSWER]

b)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    50      
u = mean =    38.2      
n = sample size =    10      
s = standard deviation =    5.1      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    7.316642429      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   7.316642429   ) =    1.27121*10^-13 [ANSWER]

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