What TWO properties must be satisfied by a continuous probability distribution / probability curve?

2.Explain what the meantells us about a normal curve, and explain what the standard deviationtells us about a normal curve.(focus on the height of the peak/ how wide or narrow the curve is)

3.Explain how to compute the z value. Start with the formula.Tell us what each variable means. Then, explain what the z value tells us about the value of the random variable.

4.Let x be a normally distributed random variable with=27 and =4. Find the z value for each of the following observed values of x:Round to TWO decimal places if needed.

a.X = 25

b.X = 28

c.X = 30

d.X = 38

e.X = 46

5. In #4,

a.which response (a, b, c, d, e) is the most uncommon due to how far it is from the mean?

b.which response(s) are within one standard deviation of the mean?

6.If the random variable z has a standard normal distribution,sketchand find each of the following probabilities.You may need to reference an online z table.

a.P( 0< z <1.5)

b.P( z> 2)

c.P( z< 1.7)

d.P( z< -1.6)

7.Weekly demand at a grocery store for a brand of breakfast cereal is normally distributed with a mean of 900 boxes and a standard deviation of 50 boxes. What is the probability that the weekly demand is:

a.960 boxes or less?

b.More than 1005 boxes?

c.Between 800 and 850 boxes?

8.In each of the following cases, determine whether the sample size n is large enough to say that the sampling distribution of p (p hat) is a normal distribution.

a.P=0.4; n=100

b.P=0.1; n=10