Please explain how to SOLVE IN EXCEL Sophia has picked 10kg of blackberries. She
ID: 3196040 • Letter: P
Question
Please explain how to SOLVE IN EXCEL
Sophia has picked 10kg of blackberries. She intends to make jam with them. She will donate the jam to her local youth club which will sell the jam on its market stall to raise funds. To make the jam, Sophia will need a kilogram of sugar and 400 millilitres of water for each kilogram of blackberries. She fills 45 jars, and each jar will be sold for £2.85. (a) The contents of each jar follow a normal distribution with mean weight 360 grams and a standard deviation 8 grams. Find the probability that the weight of jam in a jar is more than 366 grams. (b) The label on the jar indicates that the minimum weight of the jam in the jar is 340 grams. Can this claim be justified? Show your working clearly.
Explanation / Answer
a) The contents of each jar follow a normal distribution with mean weight (u) = 360 grams and
a stand deviation (s) of 8 gramhs;
We are to find the probability that the weight of the jar is > 366 grams;
We use the formula of z value to calcualte the probability
zx = (x-u) / s = (366-360) / 8 = 6/8 = 0.75
So we are to find the chances of a value being z>0.75 in a normal curve;
We see that a z value of 0.75 has a standard normal probability of = 0.7734;
Thus, probability of a value being > 0.75 = 1-0.7734 = 0.2266
Thus, probability of weight of jam in a jar being more than 366 grams is = 0.2266
b) The label states that minimum weight of the jar is 340 grams;
We find the z vlaue of 340 and we get
z = (340-360) / 8 = -20//8 = -2.5
We see that z = -2.5 covers an area of = 0.0062 or 0.62% ;
Thus, at a 99% level of significance we can fairly state that minimum weight of the jar is 340 grams;
This claim will not be true for a levle of significance > 99.38%