A peanut butter seller sells an average of 250 bottles of 1 kg week with a standard deviation of 42 kg. The sales are normally distributed.
a) If a sample of 16 weeks was selected for a study, find the probability that the sample mean is greater than 300 bottles
b) In one year how many weeks would record sales of less than 150 bottles
a) "P(\\bar X>300)=P(Z>\\frac{300-250}{\\frac{42}{\\sqrt{16}}})=P(Z>4.76)=1-P(Z<4.76)<0.0001."
b) "P(X<150)=P(Z<\\frac{150-250}{42})=P(Z<-2.38)=0.0087."
Number of weeks: "N=52*0.0087\\approx 0.45<1."
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