A garden shop sells top soil that is sold by the cubic yard. When a customer buy

Question

A garden shop sells top soil that is sold by the cubic yard. When a customer buys a cubic yard a front loader is used to scoop the top soil from the storage bin and transfer it to the customer’s truck; thus the amount transferred to the truck is an approximation. On average the weight of the top soil transferred to a truck is 2,150 lbs. with a standard deviation of 19 lbs. The weight is normally distributed. In a single day, top soil is sold to eight customers. What is the probability that the average weight sold is less than 2,130 lbs.? Round your answer to the ten-thousandths place.

Explanation / Answer

Mean is 2150 and s is 19, N is 8 therefore standard error is s/sqrt(N)=19/sqrt(8)=6.718

z is given as (x-mean)/s

Thus P(x<2130)=P(z<(2130-2150)/6.718)=P(z<-2.98) or 1-P(z<2.98)

from normal distribution table we get 1-0.9986 =0.0014

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