Dentists\' use of anesthetics. A study published in Current Allergy & Clinical I

Question

Dentists' use of anesthetics. A study published in Current Allergy & Clinical Immunology (Mar. 2004) investigated allergic reactions of dental patients to local anesthetics. Based on a survey of dental practitioners, the study reported that the mean number of units (ampoules) of local anesthetics used per week by dentists was 79, with a standard deviation of 23. Consider a random sample of 100 dentists, and let x represent the mean number of units of local anesthetic used per week for the sample.

a) What is x?

b) What is x?

c) Find the z-score for the value x = 80 ampoules.

d) Find P(x > 80).

Explanation / Answer

a)

By central limit theorem, it has the same mean,

ux = u = 79 [ANSWER]

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b)

Also,

sigma(X) = sigma/sqrt(n) = 23/sqrt(100) = 2.3 [ANSWER]

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c)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    80      
u = mean =    79      
n = sample size =    100      
s = standard deviation =    23      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    0.434782609   [ANSWER]

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d)

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    80      
u = mean =    79      
n = sample size =    100      
s = standard deviation =    23      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    0.434782609      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.434782609   ) =    0.331860115 [ANSWER]
  

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