2. (3) Farmers are delivering fresh vegetables to a frozen vegetables supplier.

Question

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 interval

Explanation / Answer

a = 5 b = 6 Amount Delivered 120 140 160 180 200 220 Number of days 5 34 92 50 14 5 a) Mean 164.9 b) Confidence level 0.94 Std Dev 20.4 Z value for 0.47 1.88 Sample size 200 Confidence Interval Min Mean - Z*(Std dev) Max Mean + Z*(Std dev) Confidence interval is Min 126.548 Max 203.252 c) Probability of atleast 195 kilos delivered in a day Z 1.47549 Probability of atleast 195 kilos includes region less than that P value for above z 0.4306 Therefore total probability is 0.9306 Percentage 93.06%

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