Answer to Question #284649 in General Chemistry for Brian

Question #284649

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



1
Expert's answer
2022-01-05T08:47:02-0500

a) Find the probability:


"P(\\mu_s>300)=P(Z>\\frac{300-250}{\\frac{42}{\\sqrt{16}}})=P(Z>4.76)=1-P(Z<4.76)<0.0001."


b) To determine the number of weeks, find the corresponding probability:


"P(X<150)=P(Z< \n42\n150\u2212250\n\u200b\n )=P(Z<\u22122.38)=0.0087.\\\\\\space\\\\\nN=52\\cdot0.0087\u22480.45<1."


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