Hello here are some business statistic questions I have for you.

Q1. A microwave manufacturing company has just switched to a new automated production system. Unfortunately, the new machinery has been frequently failing and requiring repairs and service. The company has been able to provide its customers with a completion time of 6 days or less. To analyze whether the completion time has increased, the production manager took a sample of 25 jobs and found that the sample mean completion time was 6.5 days with a sample standard deviation of 1.5 days. At significance levels of .05, test whether the completion time has increased. Show the hypotheses, the critical and calculated values of the test statistic and perform the test.

Q2. If x is a binomial random variable where n=100 and p= 0.30 find the probability that x is greater than or equal to 35 using normal approximation to the binomial. Discuss whether continuity correction is required or not.

Q3.A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results.

X=24

X^2 = 124

Y = 42

Y^2 = 338

XY=196

Calculate the coefficient of determination and the coefficient of correlation between X and Y. Interpret the coefficient of Determination. Also find the slope and intercept and interpret the estimated regression equation. What would the predicted sales of tires be if he spends five thousand dollars in advertising? Perform test of significance for the slope coefficient. Use 5% level of significance.

Q4. The diameter of small nerf balls manufactured at a factory in China is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of 0.08 inches. Suppose a random sample of 20 balls are selected. What percentage of sample means will be less than 5.15 inches?

Thank you for your time and effort!