Question

re than 52 hours? the sample average is less than 47...


According to a study, the average number of hours of TV viewing per household per week in the Philippines is 50.4 hours and the standard deviation is 11.8 hours. If a random sample of 42 households is taken, what is the probability that-

  • the sample average is more than 52 hours?
  • the sample average is less than 47.5 hours?
  • the sample average is less than 40 hours?

Answer

The mean of the number of hours of TV viewing per household per week in the Philippines is,

μ= 50.4 hours.1

The standard deviation is , σ=11.8 hours.

The sample given is 6.

The new standard deviation is,

σ¯=11.842=1.820779.

 

a. The probability that the sample average is more than 52 hours is,

PX¯>52=PZ>X-μσ=PZ>52-50.411.842=PZ>1.61.820779=PZ>0.88=0.1894.

b. The probability that the sample average is less than 47.5 hours is,

PX¯<47.5=PZ<X-μσ=PZ<47.5-50.411.842=PZ<-1.59=0.0559.

c. The probability that the sample average is less than 40 hours is,

PX¯<40=PZ<X-μσ=PZ<40-50.411.842=PZ<-5.71=0.

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