Sample Proportions. 1. Assume that you have a weighted coin with the probability

Question

Sample Proportions.

1. Assume that you have a weighted coin with the probability of getting a head equal to 3/4 (ie. probability(head) = 0.75).

(a) What is the mean for the sampling distribution for all samples of size n = 100 flips this weighted coin?

(b) what is the standard deviation for the sampling distribution for all samples of size n = 100 flips for this weighted coin?

(c) what is the probability of getting at least 70 heads (ie. 70 or more) with this weighted coin out of a random sample of size n = 100 flips?

(d) what is the probability of getting less than 70 heads with this weighted coin out a random sample of size n = 100 flips?

Explanation / Answer

A)

As n = 100, p = 0.75,

u = mean = np =    75 [ANSWER]

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b)
  
s = standard deviation = sqrt(np(1-p)) =    4.330127019 [ANSWER]

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c)

We first get the z score for the critical value:          
          
x = critical value =    69.5      
u = mean = np =    75      
          
s = standard deviation = sqrt(np(1-p)) =    4.330127019      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    -1.270170592      
          
Thus, the right tailed area is          
          
P(z >   -1.270170592   ) =    0.897988065 [ANSWER]

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d)

We first get the z score for the critical value:          
          
x = critical value =    69.5      
u = mean = np =    75      
          
s = standard deviation = sqrt(np(1-p)) =    4.330127019      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    -1.270170592      
          
Thus, the left tailed area is          
          
P(z <   -1.270170592   ) =    0.102011935 [ANSWER]

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