normally distribution population

Question

RTK Antigen Test is carried out to detect viral proteins related to the Covid-19 virus to determine active infection. Since September 2021, Malaysia government has set the maximum ceiling prices for self-test kit. The pricing was made to ensure the kits are affordable for public. Based on the recent survey about the price for this product, on average the self-test kits was sold at RM16.11 with a standard deviation of RM1.56. A random sample of 16 available brands in the market have been selected from a normally distributed population. i. What is the probability that the mean price of this sample is more than RM17? (4 marks) ii. How likely is it the mean price of self-test kits obtained from this sample will be within RM1 of the population mean? (4 marks) iii. What is the value of 𝑥̅to the right of which 33% of the means computed from this random sample of 16 self-test kits would fall? (3 marks) iv. Construct a 97% confidence interval for the true mean price for all self-test kits brand. (4 marks)

Answer 1

I) standard deviation of mean distribution = 1.56/sqrt(16) = .39. Use normal cdf function on TI84. normalcdf(mean=16.11, sdv = .39, 17, 10⁹) = .011

II) normalcdf(mean=16.11, sdv = .39, 15.11, 17.11) = .9897

III) inverse norm (area to left = .67, mean = 16.11, sdv = .39) = 16.28

IV) T internal stats function (mean = 16.11, sdv = .39, n=16, level=.97) =

(5.88, 16.34)