1. You are told that the weights of bags of almonds are normally distributed with a mean of 500 grams and a standard deviation of 44.49 grams.According to the Empirical rule, within what range will approximately 68% of the bags of almonds weigh?Please give your first answer as the lower bound and your second answer as the upper bound.Give your answers correctly roundedto two decimal places.Do NOT include units in your answers.

2. If xbar= 30, s=2 and n=25give the lower confidence limit and the upper confidence limit, for a 90% confidence interval to estimate the population mean .Calculate upper and lower confidence limit. Please give your answer correctly rounded to two decimal places and do NOT include units in your answer.

3. A nutritionist created a 95% confidence interval to estimate the average amount of sugar (grams) consumed by an individualper day (19.4, 61.5) grams.What is the value of the width of this confidence interval?Please give your answer correctly rounded to two decimal places and do NOT include units in your answer.

4. An electricity provider wants to estimate the mean time it takes for customers to get an electrical fault resolved. The provider took a random sample of 25 customers who had recently reported an electrical fault and found a mean time of 22.29 hours.Assume the population standard deviation is 0.29 hours. What is the value of the margin of error for a 95% confidence interval?Please give your answer correctly rounded to two decimal places and do NOT give units.

5. The production manager at a textile mill, believes that a new machine, producing cloth, is not workingaccording to the company's specifications.The company requires that the cloth should have a mean breaking strength of 10 Kg.A sample of 66 pieces of cloth reveals a sample mean breaking strength of 12.6 Kg and a standard deviation of 0.7 Kg. The manager wants to do a hypothesis test of the mean.What value of the mean would be used in the null and alternative hypotheses?

6. Production managers, on an assembly line, must monitor the output to check that they are manufacturing more than an average of 100 parts per production run. They continuously inspect a random sample of production runs and find the average number of parts manufactured.The hypotheses are:

Ho: = 100

Ha: > 100

Say a random sample of 36 production runs is taken, where the mean number of parts manufactured is found to be 108 parts with a standard deviation of 5 parts.If testing at the 10% level of significance, what is the critical value?Please give your answer correctly rounded to two decimal place.