Hello I would like to have the detailed answers for these questions please so I can start practicing for my exam :)

Q1

Work with the Rennes province to improve health care, by establishing a Covid19 test. Patient Wait Time for test appointment is normally distributed with a mean of 28 hours and a standard deviation of 7 hours.

a) What proportion of Patient Wait Times take between 20 hours and 40 hours?

b) What proportion of Patient Wait Times longer than 25 hours?

c) What is the Patient Wait Time such that only 15% of tests are faster?

d) What is the Patient Wait Time such that only 25% of tests are more tardily?

Q2

The mayor of Rennes city has compiled data on the amount spent by the patients to buying the protective mask and hand sanitizer gel. The data collected indicate that the amount spent of Population (P) 12000 patients follows a normal distribution

The data scientist of Rennes city council confirms at 99% confidence level, the confidence interval of the amount spent by the patients in the population (P) is between [ 13,4 ; 116,6 ]

a) Using the data scientist information, determine the population mean () and the population standard division ().

The data scientist chose from the population (P) a random sample (S1) of 1000 patients.

b) Estimate at 95% confidence level, the mean age of patients in the sample (S1).

Suppose the mayor chose from the population (P) a random sample (S2) of 610 patients, and he claims, at the 99% confidence level, the amount spent mean in the sample (S2) is between [ 58,85 ; 85, 58].

c) What do you say to this statement? Justify your answer (5 lines max).

Q3

If you are 11 or older and live in France, you can use the TousAntiCovid contact tracing app. By using it you will help stop or slow the spread of coronavirus.

Rennes Health Centre Manager followed intensely the free App download. From a population (P) of 10.000 Rennes households, a random sample (S1) of 800 households was selected for a telephone survey. The key question asked was, "Do you or any member of your household use the TousAntiCovid contact tracing app. Of the 800 respondents, 450 said yes and 350 said no.

a) Determine at 95% confidence level, the population proportion of Rennes households (P) use the TousAntiCovid contact tracing app.

Suppose the proportion in the population of all household use the TousAntiCovid app equals 45%, and accuracy level will be within + 4%.

b) At 95% confidence level, determine the sample size n.

The mayor of Rennes city claims that in the population (P) the test results will be available in 72 hours. If population standard division equal to 14 hours and random sample (S1) have a mean time of 71 hours.

c) Test the hypothesis that the average of time is 72 hours at the 5% significance level.

d) Test the hypothesis that the average of time is greater than or equal to 72 hours at the 1% significance level.