Question 3 A cup of strawberry-flavor yoghurt has the weight, which is normally distributed with the...

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Question 3 A cup of strawberry-flavor yoghurt has the weight, which is normally distributed with the mean of 150 grams and the standard deviation of 0.2 grams. A cup of mango-flavor yoghurt has the weight, which is normally distributed with the mean of 140 grams and the standard deviation of 0.1 grams. The cup weights are independent. A customer buys a pack of 4 cups of strawberry yoghurt and a pack of 4 cups of mango yoghurt. Please find the followings: 3.1 If the customer takes one cup of strawberry yoghurt, what the probability that the cup has the weight greater than 150.1 grams? 3.2 What the probability that the average cup weight of the pack of 4 strawberry yoghurt cups is greater than 150.1 grams? 3.3 Why the probability in question 3.2 is less than the probability in question 3.1? 3.4 What is the probability that the average cup weight of the pack of 4 strawberry yoghurt cups is larger than the average cup weight of a pack of 4 mango yoghurt cups by at least 10.3 grams? 3.5 If 3 cups of strawberry yoghurt and 2 cups of mango yoghurt are sampled, what is the probability that the sum of the weights of these 5 cups is greater than 731 grams? Question 4 Now let's consider the sales revenue of the two flavors of yoghurt products in question 3. The price of a cup of strawberry yoghurt is 12 baht while the price of a cup of mango yoghurt is 10 baht. The mean and standard deviation of the daily sales volume (unit of cups) of the two flavors are shown in the table below. The sales volumes of these two products are independent. Flavor Mean (cups) Standard Deviation (cups) Strawberry 100 3 Mango 60 4 4.1 Find the expected sum of sales revenue from these two products. 4.2 Find the standard deviation of the sum of sales revenue from these two products. 4.3 Find the probability that in a given day, the sum of sales revenue from these two products is less than 1,700 baht. Question 3 A cup of strawberry-flavor yoghurt has the weight, which is normally distributed with the mean of 150 grams and the standard deviation of 0.2 grams. A cup of mango-flavor yoghurt has the weight, which is normally distributed with the mean of 140 grams and the standard deviation of 0.1 grams. The cup weights are independent. A customer buys a pack of 4 cups of strawberry yoghurt and a pack of 4 cups of mango yoghurt. Please find the followings: 3.1 If the customer takes one cup of strawberry yoghurt, what the probability that the cup has the weight greater than 150.1 grams? 3.2 What the probability that the average cup weight of the pack of 4 strawberry yoghurt cups is greater than 150.1 grams? 3.3 Why the probability in question 3.2 is less than the probability in question 3.1? 3.4 What is the probability that the average cup weight of the pack of 4 strawberry yoghurt cups is larger than the average cup weight of a pack of 4 mango yoghurt cups by at least 10.3 grams? 3.5 If 3 cups of strawberry yoghurt and 2 cups of mango yoghurt are sampled, what is the probability that the sum of the weights of these 5 cups is greater than 731 grams? Question 4 Now let's consider the sales revenue of the two flavors of yoghurt products in question 3. The price of a cup of strawberry yoghurt is 12 baht while the price of a cup of mango yoghurt is 10 baht. The mean and standard deviation of the daily sales volume (unit of cups) of the two flavors are shown in the table below. The sales volumes of these two products are independent. Flavor Mean (cups) Standard Deviation (cups) Strawberry 100 3 Mango 60 4 4.1 Find the expected sum of sales revenue from these two products. 4.2 Find the standard deviation of the sum of sales revenue from these two products. 4.3 Find the probability that in a given day, the sum of sales revenue from these two products is less than 1,700 baht.