It is known from past experience that the life of traffic light bulbs is normall

Question

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

Explanation / Answer

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]

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