Please show the formula and step-by-step process to the solution and explain

3. a) State the mean and standard deviation of the standard normal curve. b) Find the z-score for which 90% of the distribution's area lies between -z and z.

c) Extending the meaning in part b, only 5% of z-scores would lie above ________

7.a) Given a normal distribution with = 60 and = 10, what random variable (x) corresponds to the 98thpercentile?Conclude your post with: Only 2% of x values will be above ______.

b) Given a normal distribution with = 60 and = 20, what random variable (x) corresponds to the 98thpercentile?Conclude your post with: Only 2% of x values will be above ______.

8. Given a normal distribution with = 60 and = 10, complete the following:

a) Find the z-score that corresponds to x = 45. Does the z-score indicate that 45 is a usual or unusual data value in this data set? Make sure to explain your reasoning.

b) Is 45 inside or outside two standard deviations from the mean? Does this indicate that 45 is a usual or unusual value? Explain.

c) Find the probability that x is less than or equal to 45. Does this indicate that 45 is a usual or unusual value? Explain.