Download Z-Scores and the Normal Distribution

Z-Scores and the Normal Distribution
Name ________________________________
1. A physics professor uses the normal distribution to assign final grades. If μ  76 and σ  7 …..
(a) covert the following scores to z-scores: 82, 64
(b) convert the following z-scores to grades: 1.9, -0.4
2. Use the normal distribution chart to find the following:
(a) P ( Z  1.42 )
(b) P( Z  0.78)
(c) P(0.21  Z  2.08 )
(d) P(1.81  Z  2.25)
3. The height of young women is approximately normally distributed with μ  64.5 inches and
σ  2.5 inches. Find the probability that a given woman will be…..
(a) shorter than 68 inches.
(b) taller than 60 inches.
(c) between 63 and 67 inches.
(d) What height falls at the 40th percentile?
(e) What height are only 5% of young women taller than?
4. Blood cholesterol levels increase the risk of heart disease. The levels in 14-year-old boys are normally
distributed with μ  170 mg/deciliter and σ  30 mg/deciliter. Find the probability that a boy will have a
cholesterol level…..
(a) over 200.
(b) under 180.
(c) between 155 and 190.
(d) It is necessary for a boy to receive medical attention if his cholesterol level is over 240 mg/dl.
What proportion of boys will need medical attention?
(e) What level falls at Q3?
(f) What level are only 7% of 14-year-old boys greater than?
5. Verbal SAT scores are normally distributed with N(505, 110). Find the probability that a student will
obtain a score that is…..
(a) above 630.
(b) below 470.
(c) between 520 and 590.
(d) How high must a student score to be in the top 10% of all verbal SAT scores?
(e) What must a student score to be at the median score?
(f) What must a student score to be at the 20th percentile?
6. The life expectancy of wood bats is normally distributed with a mean of 60 days and a standard deviation
of 17 days.
(a) What is the probability that a randomly chosen bat will last at least 60 days?
(b) What percentage of bats will last between 40 and 80 days?
(c) What is the probability that a bat will break during the first month?
7. Given a normal distribution with a mean of 115, find  if 6% of the values fall below 75.
8. Given a normal distribution with a standard deviation of 15, find  if 15% of the values fall above 80.
9. If 30% of the data in a normally distributed population fall below 230 and 60% fall below 244, find
 and  .
10. On the driving range, Tiger Woods practices his swing with a particular club by hitting many, many
balls. When Tiger hits his driver, the distance the ball travels follows a Normal distribution with mean
304 yards and standard deviation 8 yards. What percent of Tiger’s drives travel …..
(a) at least 290 yards.
(b) less than 300 yards.
(c) between 295 and 310 yards.
(d) Find the distance at which only 3% of Tiger’s drives exceed.
(e) Find the distance at which only 10% of Tiger’s drives are below.
(f) Suppose Tiger’s standard deviation was unknown. If the mean was still 304 yards, and a drive at
the 95th percentile was 313 yards, find the new standard deviation. Based on this result, has Tiger
become more or less consistent with his drives?