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

• What two properties must be satisfied by a continuous probability distribution / probability curve?
• Explain what the mean µ tells us about a normal curve, and explain what the standard deviation σ tells us about a normal curve.
• Explain how to compute the z value. What does the z value tell us about the value of the random variable?
• Let x be a normally distributed random variable with µ=30 and σ=5. Find the z value for each of the following observed values of x:
  a. X = 25
  b. X = 15
  c. X = 30
  d. X = 40
  e. X = 50
• If the random variable z has a standard normal distribution, sketch and find each of the following probabilities.
  a. P( 0 < z 2)
  c. P( z < 1.7)
  d. P( z < -1.6)
• Weekly demand at a grocery store for a brand of breakfast cereal is normally distributed with a mean of 800 boxes and a standard deviation of 75 boxes. What is the probability that the weekly demand is:
  a. 960 boxes or less?
  b. More than 1005 boxes?
  c. Between 750 and 850 boxes?
• What does the Central Limit Theorem tell us about the sampling distribution and sample mean?
• 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
  c. P=0.1, n=50