Key 3 - Practice Quiz No. 3

1. The playing life of a MCA radio is normally distributed with a mean of 600 hours and a standard deviation of 100 hours. (4 points each section)

a) Draw the distribution showing up to plus and minus 3 standard deviations. Note on the axis the corresponding Z values for the X values.






 
 
  1. What is the probability that a radio selected at random will last from 550 to 720 hours? Draw the relevant area on the curve.







 
 
  1. The radio costs $10 and MCA sells 1 million radios a year. As a selling point, MCA wants to guarantee 400 hours of play or MCA will replace the radio for free.

Show the area on the curve relating to the radios which will have to be replaced:

 

What is the probability that a radio will have to be replaced?



 

What will be the cost per year to MCA?

.





 
2. In a random sample of 62 professional actions, it was found that 39 were extroverts. Find the 99% confidence level for the population proportion of actors who are extroverts. (10 points total)

Sample proportion:

N:

Standard error: . 

 

What is the margin of error?

 

Interpret the results:

 
3. Bellevue Burger is a franchise chain of 100 stores. A random sample of 8 stores shows the following profit for 1996: (5 points each section)

61,242

28,785

92,203

10,404

76,326

96,803

91,053

67,422

Calculate the mean of the sample.


 

Calculate the standard deviation.

 

 

Draw the distribution of up to plus and minus 3 standard errors of the mean.

.Standard error:

 

What is the 90% confidence level?

Interpret the results:

 

 
   In a city, public health officials want to estimate the proportion of the population of children (grades 1-8) who need eye glasses. In the past, they have found that 230 out of 1,000 children need glasses. The health department drew a sample size of 1310 for a margin of error of 3%. What is the confidence level associated with this sample size?

 

Proportion: .

Bound: .

Standard error:

 

Confidence level:

 

 
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