2. Farmers are delivering fresh vegetables to a frozen vegetables supplier. Beca

Question

2. 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(m; ) 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 200 220 Amounts delivered x120 140 40 180 48 160 Number of days ni Using this sample, a) calculate the point estimate to the population expectation m (the sample mean) b) at the confidence level of = 0.98, calculate the interval estimate to the expectation when the population standard deviation is known to be 20.2 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 The 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

Amount delivered 120 140 160 180 200 220 Number of days 5 40 88 48 18 5 a) Sample Mean 164.8039216 Standard dev of population 20.2 Sample size 204 14.28286 b) Interval estimate Confidence level 0.98 Z 2.33 Min Sample mean - Z * Std dev of population / Sqrt sample size 117.7379 Max Sample mean - Z * Std dev of population / Sqrt sample size 211.8699 c) Atleast 195 z = (195 - mean) / std dev Z 1.494855 p value 0.9332 The probability of atleast 195 kgs is 0.9332 Lower Upper Margin of Error Population expectation 3.295279 159.3732 170.2347 Confidence interval 3.295279 Min 113.8581 121.6177 Max 204.8882 218.8516

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