Please provide work out steps for each of the following questions.

Q1. A primary school wants to monitor the lengths of pencils in its kindergarten classes, in order to place orders for new pencil sets at the right time. In a recent study, the school found that, after one term of use, the lengths of pencils followed a normal distribution with mean 8.1cm and standard deviation is 0.83 cm.

A sample of 4 One-term-old pencils are randomly selected from a class

Answer the following questions, keeping in mind that your answer must be a number between o and 1. ie., do not use percentages, Give your final answer with a least 3 dp.

Compute the probability that the mean length of pencils for the selected is more than 8.06cm _____________

Q2. A random sample of 32 meals offered at Macquarie Centre is selected and tasted by a food critic and 16 are found to be delicious.

Compute a 95% confidence interval for the true proportion of delicious meals among those sold at the Macquarie Centre, Give your final answer with at least 3 dp.

Lower Bound of 95% Cl (smaller number here)

Upper bound of the 95% Cl (bigger number here)

Q3. The library at UCLA has a vast selection of Statistics books. We can assume that is has all the books over published in the discipline. A sample of 27 Statisitics books are selected from Library. The histogram of y, the weights of the books, looks normal. The sample mean `y is equal to 1.46kg and the sample standard deviation s is equal to 0.52kg

Compute a 95% confidence interval for the true proportion of delicious meals among those sold at the Macquarie Centre, Give your final answer with at least 3 dp.

Lower Bound of 95% Cl (smaller number here)

Upper bound of the 95% Cl (bigger number here)

Q4. The proportion of UCLA students who think that learning at tertiary education level is highly beneficial for successful employment is 0.58

Answer the following question, keeping in mind that your answer must be a number between 0 and 1, I,e., do not use percentages give your final answer with at least 3 dp.

What is the probability that out of 52 UCLA students, 34 or more thinking that their studies will be highly beneficial for successful employment? _______

Q5. Stoaches are fictional creatures, sometimes mistaken for mome raths. Suppose a two-tailed -test is conducted to test for a difference between the population means of adult female stoach weights and adult male stoach weights. The female sample has 5 weights, and the male sample has 14 weights. The -statistic for the test is 0.48637. What is the -value? (Give your answer to 4 decimal places.) -value:

Q6

The daily dose of a medication, in grams, for a patient is a function of the age , in years, of the patient. So we have =(). The derivative of is . What are the units of ? Select one: a. grams per year b. years per gram c. grams d. years e. does not have units

Q7. The battery life in stand-by mode of a 2-year-old iPhone 6 follows a normal distribution with mean 7.31 days and standard deviation 0.94 days.

A sample of 9 2-year-old iPhone 6s are randomly selected

Answer the following question, keeping in mind that your answer must be a number between 0 and 1 i.e., does not use percentages. Give your final answer with at least 3 dp.

Compute the probability that the mean battery life for the selected sample is more than 7.27 days.