According to a sample of 435 American adults, the time spent watching television

Question

According to a sample of 435 American adults, the time spent watching television per day can be modeled using the normal distribution with a mean of 6.3 hours and a standard deviation of 1.6 hours. (a) If you randomly sample one American adult, what is the probability that he or she watches more than 8.2 hours of television per day? (b) If you select a random sample of 435 American adults, what is the probability that the average time spent watching television is less than 6.4 hours per day? (Use 4 decimals.) Enter a number. (Use 4 decimals.)

Explanation / Answer

Mean is 6.3 and s is 1.6

a) P(x>8.2)= P(z>(8.2-6.3)/1.6)=P(z>1.19)=1-P(z<1.19) , from normal distribution table we get 1-0.8830=0.117

b) P(x<6.4)=P(z<(6.4-6.3)/(1.6/sqrt(435)))=P(z<1.3) thus 0.9032

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