According to medical data, the probability than an adult US citizen has been dia

Question

According to medical data, the probability than an adult US citizen has been diagnosed with high cholesterol is 15%. Suppose you randomly select 65 adults and ask if he or she has been diagnosed high cholesterol. Decide whether you can use the normal distribution to approximate the binomial distribution. If so, find the mean and standard deviation. Round to the nearest hundredth when necessary. If not, please explain why a normal distribution should not be used. Find the probability that no more than 10 of the sampled adults have been diagnosed with high cholesterol.

Explanation / Answer

39.

As n = 65, p = 0.15,

np = 65*0.15 = 9.75 > 5
n(1-p) = 65*(1-0.15) = 55.25 > 5

As both quantities are greater than 5, YES, IT IS APPROPRIATE TO USE NORMAL APPROXIMATION.

Hence,

u = mean = np =    9.75 [ANSWER]
  
s = standard deviation = sqrt(np(1-p)) =    2.878801834 [ANSWER]

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b)

We first get the z score for the critical value:          
          
x = critical value =    10.5      
u = mean = np =    9.75      
          
s = standard deviation = sqrt(np(1-p)) =    2.878801834      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    0.260525053      
          
Thus, the left tailed area is          
          
P(z <   0.260525053   ) =    0.602770604 [ANSWER]

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