Please answer, really need help. A particular pharmaceutical company BioVita Vit

Question

Please answer, really need help. A particular pharmaceutical company BioVita Vitamin C supplements in batches of 1 million capsules. The FDA announced a neew regulation thta the average Vitamin C concentration for any batch of Vitamin C pills has to be = 60 mg. Last week, an FDA inspector audited BioVita by taking a random sample of 18 pills from a batch and measured the Vitamin C Concentrations in each. The concentrations (in mg) were: 59 66 66 68 60 58 44 83 68 75 57 49 69 78 59 55 72 80 Compute the 5-point summary for this data. 11. Refer to Question 10. In addition to the above information, the FDA inspector also computed the sample's mean (64.8mg), standard deviation (10.6 mg) standard error of the mean (2.5mg), and 95% confidence interval (59.5mg to 70.0mg). Assuming that this batch's vitamin C concentration follows a normal distribution, please select which of the following statements is true. a) This batch does not violate the 60 mg FDA regulation b) The probability that an individual pill's vitamin C concentration is > 64.8mg is 50% c) This batch violates the 60 mg FDA regulation d) None of the above

Explanation / Answer

10.We can obtain the 5 point summary by using the following code in R

x=c(59,66,66,68,60,58,44,83,68,75,57,49,69,78,59,55,72,80)
boxplot(x)
summary(x)

We will get as output

Min. 1st Qu. Median 3rd Qu. Max.
44.00 58.25 66.00 71.25 83.00

11.Here 95% Confidence interval for the sample mean is (59.5 , 70)

Here the sample mean is 64.8 So

a) This batch does not violate the 60 mg FDA regulation

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