Question

a peanut butter seller sells 250 bottles on average per week with a standard deviation of 42kg.the nsales are normally distributed.one one year how many weeks would record sales of less than 150 bottles

Answer 1

$\mu=250.\space \sigma=42$

Let $X$ be a random variable representing the sales of peanuts made.

Therefore, we first determine the probability that sales of peanuts made is less the 150.

So,

$p(X\lt150)=p(Z\lt(150-\mu)/\sigma)=p(Z\lt (150-250)/42)=p(Z\lt-2.38)$

Using standard normal tables,

$p(Z\lt-2.38)=\phi(-2.38)=0.0087$

Therefore, the probability that sales of peanuts made in a week is less than 150 is 0.0087.

Now, there are approximately 52 weeks in a year, to find the number of weeks in a year that the sales of peanuts made is less 150, we multiply the number of weeks with the probability as follows.

Number of weeks=0.0087*52=0.4524$\approx 1week.$

Therefore, in a year, the number of weeks that would record sales of less than 150 bottles is 1 week.