It is known from past experience that the life of traffic li

It is known from past experience that the life of traffic light bulbs is normally distributed with a standard deviation of 270 hours. In a study, if it is required to be 90% certain that the mean estimate is within 115 hours of the population mean. How many light bulbs should be selected for the study 3 4 14 15 A student takes a 20-question exam. The time that he needs to solve each problem is randomly distributed with mean of 5 minutes and standard deviation of 1.1 minute. What is the probability that he finishes the exam in less than 105 minutes 0.15 0.50 0.75 0.85

Solution

5.

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.05  
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
s = sample standard deviation =    270  
E = margin of error =    115  
      
Thus,      
      
n =    14.91373292  
      
Rounding up,      
      
n =    15   [ANSWER, D]

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6)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value = 105/20 =   5.25      
u = mean =    5      
n = sample size =    20      
s = standard deviation =    1.1      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    1.016394535      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   1.016394535   ) =    0.845279227 = 0.85 [ANSWER, D]