Hi I need help.

1. In a car assembly plant, the time it takes to assemble a car is normally distributed with a mean of 18 hours and a standard deviation of 4 hours. Calculate the probability of a car being assembled in less than 16 hours.

2. At Lilly's Medical Center, the time that Dr. Lilly spends with her patients is exponentially distributed where = 0.20. Use the information given above to answer the questions that follow: a) Calculate the mean and standard deviation of the time that Dr. Lilly spends with her patients. b) What is the probability that Dr. Lilly will see the patients between 5 and 15 minutes? 3. In Smithville, data from different shoe outlets revealed that the average sales of shoes are $868 per shoe outlet. There were 88 outlets taken as a sample for a survey where the mean calculated was $25.6, and standard deviation was known to be $2.80. a) Using the above data, calculate a 95% confidence interval for the average sale of shoes. b) Using the answer that you have found in part (a) above, illustrate the confidence intervals using a standard normal distribution graph (Bell shaped curve).

4. Tinkerbell's Jewelry Shop did a survey on its customers and it was revealed that 10 out of 30 customers had failed to comply with COVID - 19 regulations. Using the above data, answer the questions that follow: a) Calculate a 90% confidence interval for the proportion of customers who did not comply with COVID - 19 regulations. b) Using the answer that you have found in part (a) above, illustrate the confidence intervals using a standard normal distribution graph (Bell shaped curve). 5) Rita's toy factory produces toys for toddlers that are packed into boxes. Each box contains 10 toys. A box of toys randomly selected by the company's production manager found 45% of all toys packed in the boxes are defective. Use the above information and your knowledge of binomial probability to answer the following questions. a) Calculate the mean and standard deviation. (2 marks) b) Find the probability that there are at least 8 defective toys in the box.