question 1. A random sample of2,500workers is taken from the population of 15,000 workers in a company, for which the proportion of females is 0.6. Find the standard error of sampling distribution of proportion of female workers.

question 2. The safety officers of a mining company take a simple random sampleof500employees and finds that15% of the sampled employees wear contact lenses. The safety officers may take several more samples like this. Suppose that proportion of all employees in the company who wear contact lenses is12%. What are the mean and standard deviation of the sampling distribution of the proportion of employees who wear contact lenses?

question 3. A local agricultural cooperative claims that55% of about60,000 adults in a county believe that gardening should be part of the school curriculum. However, when you take a simple random sample of300adults in the county, only50% say that they believe that gardening should be part of the school curriculum. Assuming that the agricultural cooperative's claim is accurate, what is the probability that less than50% of the sample would say that they believe that gardening should be part of the school curriculum?

question 4. There are 250 dogs at a dog show who weigh an average of 12 pounds, with astandard deviation of 8 pounds. If 4 dogs are chosen at random, what is theprobabilitythat they have an average weight of greater than 8 pounds and less than 25 pounds?

question 5. In a large university, the mean amount spent by students for cell phone service is $38.90 per month with a standard deviation of $3.64 per month. Consider a group of 44 randomly chosen university students. What is the probability that the mean amount spent by students for cell phone service is $32.00 or less?

question 6. A news report stated that 65% of vehicles sold nationally were Toyota Vitz. From 800 vehicles sold in the last month, a random sample of 100 is taken:

a. Compute the standard error of sampling distribution of proportion of vehicles sold in the last

month.

b. What is the probability that at least 70 of the vehicles in the sample were Toyota Vitz?

question 7.Let the population standard deviation is 50. If we have a sample of size 100, the standard error becomes 5. Suppose we would like to reduce the standard error to 2.5 by collecting more data. This would reduce the uncertainty in our estimate. How many extra data points are required to accomplish this scenario?