a=3 and b=4 2. (3) Farmers are delivering fresh vegetables to a frozen vegetable
ID: 3047921 • Letter: A
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a=3 and b=4
2. (3) Farmers are delivering fresh vegetables to a frozen vegetables supplier. Because of the unstable weather, the delivered amounts are random and follow a normal distribution N(mo) with the expected amount of m. Using recorded delivery data from past days, the deliveries appeared to be between 110 and 230 kilos a day. For data processing, all deliveries were sorted into intervals ]110; 130].]130;150 etc. The results are given in the following table with interval centres in the first row Amounts delivered 120 40 160 80 200 220 Number of days538-a 87+b 46ta 19-b 5 Using this sample, a) calculate the point estimate to the population expectation m (the sample mean) b) at the confidence level of -0.99-0.01b, calculate the interval estimate to the expectation when the population standard deviation is known to be = 20+0.1a c) at the same confidence level, calculate point and interval estimates to the probability (proportion) of the event 'at least 195 kilos are delivered in a day he Excel sheet must include the sample size the sample mean - - the margin of error for population expectation and the confidence interval the margin of error for probability (population proportion) and the confidence intervalExplanation / Answer
amount n p Xp 120 5 0.025 3 140 35 0.175 24.5 160 91 0.455 72.8 180 49 0.245 44.1 200 15 0.075 15 220 5 0.025 5.5 200 1 164.9 b) confidence level 0.99-0.01*4 0.95 poplation sd 20+0.1*3 20.3 margin of error 39.788 lower 125.112 upper 204.688 c) z 1.482759 P(X> 195) 0.069069 amount n p Xp 120 5 =B2/200 =C2*A2 =20+A2 35 =B3/200 =C3*A3 =20+A3 91 =B4/200 =C4*A4 =20+A4 49 =B5/200 =C5*A5 =20+A5 15 =B6/200 =C6*A6 =20+A6 5 =B7/200 =C7*A7 =SUM(B2:B7) =SUM(C2:C7) =SUM(D2:D7) b) confidence level 0.99-0.01*4 poplation sd 20+0.1*3 margin of error =1.96*F15 lower =164.9 -1.96 *F15 upper =164.9+1.96*F15 c) z =(195 - 164.9)/20.3 P(X> 195) =1-NORMSDIST(B22)
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