Question

3. Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than or greater than  

According to AccuData Media Research, 36% of televisions within the Chicago city limits are tuned to "Eyewitness News" at 5:00 pm on Sunday nights. At 5:00 pm on a given Sunday, 2500 such televisions are randomly selected and checked to determine what is being watched.

a) < 2 point > points > Find the mean

b) < 2 points > Find the standard deviation

c) < 3 points > Find the minimum” usual” value and the maximum” usual “value

d) < 2 points >Would it be unusual to find that 960 of the 2500 televisions are tuned to "Eyewitness News"? Explain. ( Hint use the result from part “c” .

Answer 1

Answer 3. Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than or greater than :

Solution:

p = 36% = 0.36

sample size, n = 2500

a) the mean:

mean = n*p

= 2500 * 0.36

= 900

∴ mean = 900

b) the standard deviation:

standard deviation, σ

σ = √(n*p*(1-p))

= √(2500*0.36*(1-0.36))

= 24

c) the minimum” usual” value and the maximum” usual “value

unusual value are less than and greater than 2 standard deviation

∴ lower limit. = mean - 2σ

= 900 - 2(24)

= 852

∴ upper limit = mean + 2σ

= 900 + 2(24)

= 948

d) Would it be unusual to find that 960 of the 2500 televisions are tuned to "Eyewitness News"? Explain.  

Therefore, 960 is unusual because it is above less than and greater than 2 standard deviation limit.