1. True or False. Justify for full credit.(a) The normal distribution curve is always symmetric to 0. (b) If the variance from a data set is zero, then all the observations in this data set are identical. (c) P(AOR A complement) =1, where A complement is the complement of A. (d) In a hypothesis testing, if the p-value is less than the significance level , we do not have sufficient evidence to reject the null hypothesis (e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set. The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.2.. What is the probability that a randomly selected person has an IQ between 85 and 115?3. Find the 90th percentile of the IQ distribution4. If a random sample of 100 people is selected, what is the standard deviation of the sample mean?5. A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence intervalestimate of the mean lifetime. Show all work. Just the answer, without supporting work, will receive no creditUse for Questions 1 and 2: A grocery store takes a random sample of 200 customers. The average check-out time is 4 minutes with a standard deviation of two minutes.1. The standard error of the mean is?2. The 95% confidence level for the true average check-out time is?3. A random sample of 244 observations has a mean of 10, a median of 12 and a mode of 33. The population deviation is known to equal 2.8. the 95.44% confidence interval for the population mean is?4. The following random sample was collected: 22 33 44 6 The 80% confidence interval for the mean is?5. A random sample of 200 people was taken. Sixty percent of the people favor President Obama. The 95% confidence interval for the true population of people who favor Obama is?