The monthly sales of packaged Milo drinks in School of Business canteen follows the normal distribution with a mean of 1,200 packages and a standard deviation of 225 package. The drink stall operator, Mr. Lim would like to establish the amount of inventory levels that he should carry such that there is only a 5% chance of running out of stock. What should the inventory level be set for the packaged milo drinks such that there is only 5% of stock-out?

The amount of cereal in boxes, packed by a particular machine, is normally distributed with mean µ gram andstandard deviation 5 gram. If the advertised weight of a box is 500 gram, find(i) the proportion of boxes that will be underweight (i.e. weight less than 500 gram) when µ = 505;(ii) the value of µ required to ensure that only 1% of the boxes are underweight.(b) As a check on the setting of the machine a random sample of four boxes is chosen and the setting changed if theaverage weight of the four boxes is less than 500 gram. Find the probability that the setting of the machine ischanged when µ = 505.

In 2003, the average stock price for companies making up the S&P 500 was $30, and thestandard deviation was $8.20 (BusinessWeek, Special Annual Issue, Spring 2003). Assumethe stock prices are normally distributed.a. What is the probability that a company will have a stock price of at least $40?b. What is the probability that a company will have a stock price no higher than $20?c. How high does a stock price have to be to put a company in the top 10%?

For a certain online store, the distribution of number of purchases per hour is approximately normal with mean 1,200 purchases and standard deviation 200 purchases. For what proportion of hours will the number of purchases at the online store exceed 1,400? 68% B 32% 16% 5% E 2.5%

Continuous Probability DistributionsNow, let’s say that QC decides to sample one more tablet. This time, it selects a tablet from Batch Y4. Based on previous knowledge, you know that Batch Y4 has a mean paracetamol level of 505 mg, and its standard deviation is 25 mg. This time, QC wants to check both the upper limit and the lower limit for the paracetamol level.What is the probability that the tablet selected by QC has a paracetamol level between 450 mg and 550 mg?

ough the packages are labeled as 8 ounces,the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces.A sample of 50 packages is selected periodically,and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces.Suppose that in a particular sample of 50 packages,the mean amount dispensed is 8.168 ounces,with a sample standard deviation of 0.059 ounce.Complete parts(a)and(b). Click here to view page 1 of the critical values for the t Distribution. Click here to view page 2 of the critical values for the t Distribution. 0· a.Is there evidence that the population mean amount is different from 8.17 ounces?(Use a 0.01 level of significance.) State the null and alternative hypotheses. H0:μ=8.17 H1μ≠8.17 (Type integers or decimals.) Identify the critical value(s). The critical value(s)is(are) (Round to four decimal places as needed.Use a comma to separate answers as needed.) ChatGPT To test whether there is evidence that the population mean amount is different from 8.17 ounces at a 0.01 level of significance, you can set up the null and alternative hypotheses as follows: Null Hypothesis (H0): The population mean amount of candies is equal to 8.17 ounces. H0: μ = 8.17 Alternative Hypothesis (H1): The population mean amount of candies is different from 8.17 ounces. H1: μ ≠ 8.17 To identify the critical value(s) for a two-tailed test at a 0.01 level of significance, you can use a t-distribution table or a calculator. Since the sample size is 50, you have 49 degrees of freedom (df = n - 1). Using a t-distribution table with 49 degrees of freedom and a significance level of 0.01 (two-tailed), you can find the critical values. Typically, for a two-tailed test at 0.01 significance level, the critical values are approximately ±2.6851 (rounded to four decimal places). So, the critical value(s) for this test are approximately ±2.6851. If the calculated t-statistic falls beyond these critical values in either the lower or upper tail, you would reject the null hypothesis.