Estimate the indicated probability by using the normal approximation as an approximation to the binomial distribution. (PROBLEMS 4 & 5) 4. Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, at least 219 are defective. 5. In one county, the conviction rate for speeding is 85%. Estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions.

4

5

Step-by-step explanation:

From the question we are told that  

    The percentage of hair dryers that are defective is p=2%  

      The  sample size is  

       The  random number is  x = 219

The mean of this data set is evaluated as

substituting values

The standard deviation is evaluated as

substituting values  

Since it is  a one tail test the degree of freedom is  

      df =  0.5

So  

Now applying normal approximation

substituting values  

From the z-table  

Considering Question 5  

The  random number is  x = 90

      The mean is  

Where  n = 100

   and  p  =  0.85

So  

The standard deviation is  evaluated as

substituting values  

Since it is  a one tail test the degree of freedom is  

      df =  0.5

Now applying normal approximation

   substituting values  

From the z-table  

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.