with complete solution typewritten much better 6-9

8. A bank auditor claims that credit card balances are normally distributed with a mean of $2,870.00 and a standard deviation of $900.00. You randomly select 25 credit cardholders. What is the probability that their mean credit card balance is less than $2,500.00? 9. There are hundreds of apples on the trees, so you randomly choose just 46 apples and get a mean weight of 86 grams with a standard deviation of 6.2 grams. The true mean weight of the hundreds of apples is likely to be between 84.21 grams and 87.79 grams with 95% confidence level. Identify the point estimate, confidence level, confidence interval, and significance level.6. The weight of 1,000 children, on average, is 50kg with a standard deviation of 5kg. Suppose the weights are normally distributed, how many children weighing between 40kg and 55kg? 7. List all possible samples of n = 3, with replacement, from the population 1,3, 5,7 Identify the sampling distribution; and calculate the mean, variance, and standard deviation of the sample means. Show your solution