6-1
Find the area under the standard normal distribution curve for:
z < 3.02
0.9987
Full-time Ph.D. students receive an average of $12,837 per year. If the average salaries are normally distributed with a standard deviation of $1500, find the probability that a student makes more than $15,000.
0.0749 or 7.49%
The average teacher's salary in Connecticut is $57,337. Suppose that the distribution of salaries is normal with a standard deviation of $7500. If 100 teachers' salaries are sampled, what is the probability that the teacher makes less than $56,000 a year?
0.0375 or 3.75%
Use the normal approximation to the binomial to find the probabilities for the specific values of X.
n=50, p=0.8, X=44
0.0516 or 5.16%
Find the area under the standard normal distribution curve:
Between z=-0.07 and z=0.49
0.2158
Find the area under the standard normal distribution curve for:
z > -1.33
0.9082
Full-time Ph.D. students receive an average of $12,837 per year. If the average salaries are normally distributed with a standard deviation of $1500, find the probability that a student makes between $13,000 and $14,000.
0.2385 or 23.85%
The average teacher's salary in Connecticut is $57,337. Suppose that the distribution of salaries is normal with a standard deviation of $7500. If 100 teachers' salaries are sampled, what is the probability that the teacher makes more than $56,000 a year?
0.9625 or 96.25%
Twenty-two percent of work injuries are back injuries. If 400 work-injured people are selected at random, find the probability that 92 or fewer have back injuries.
0.7054 or 70.54%
A report stated that the average number of times a car returns to its food bowl during the day is 36. Assuming the variable is normally distributed with standard deviation of 5, what is the probability that a cat would return to its dish between 32 and 38 times a day?
0.4435 or 44.35%
Find the area under the standard normal distribution curve for:
Between z=0 and z=2.9
0.4981
The average number of potholes per 10 miles of paved U.S. roads is 130. Assume this variable is approximately normally distributed and has a standard deviation of 5. Find the probability that a randomly selected road has more than 142 potholes per 10 miles.
0.0082 or 0.82%
The average yearly Medicare Hospital Insurance benefit per person was $4064 in a recent year. If the benefits are normally distributed with a standard deviation of $460, find the probability that the mean benefit for a random sample of 20 patients is less than $3800.
0.0051 or 0.51%
The percentage of U.S. households that have online connections is 78%. In a random sample of 420 households, what is the probability that fewer than 315 have online connections?
0.0618 or 6.18%
On the daily run of an express bus, the average number of passengers is 48. The standard deviation is 3. Assume the variable is normally distributed. Find the probability that the bus will have fewer than 42 passengers.
0.0228 or 2.28%
Use the standard normal distribution to find the probability of
P(-1.75<z<1.77)
0.9215 or 92.15%
The average number of potholes per 10 miles of paved U.S. roads is 130. Assume this variable is approximately normally distributed and has a standard deviation of 5. Find the probability that a randomly selected road has less than 125 potholes per 10 miles.
0.1587 or 15.87%
The average yearly Medicare Hospital Insurance benefit per person was $4064 in a recent year. If the benefits are normally distributed with a standard deviation of $460, find the probability that the mean benefit for a random sample of 20 patients is more than $4100.
0.4920 or 49.20%
If 8% of all people in a certain geographic region are unemployed, find the probability that in a sample of 200 people, fewer than 10 are unemployed.
0.0455 or 4.55%
On the daily run of an express bus, the average number of passengers is 48. The standard deviation is 3. Assume the variable is normally distributed. Find the probability that the bus will have more than 50 passengers.
0.2514 or 25.14%
Use the standard normal distribution to find the probability:
P(z > -3.09)
0.999 or 99.9%
The average number of potholes per 10 miles of paved U.S. roads is 130. Assume this variable is approximately normally distributed and has a standard deviation of 5. Find the probability that a randomly selected road has between 128 and 136 potholes per 10 miles.
0.5403 or 54.03%
Procter & Gamble reported than an American family of four washes an average of 1 ton (2000 pounds) of clothes each year. If the standard deviation of the distribution is 187.5 pounds, find the probability that the mean of a randomly selected sample of 50 families of four will be between 1980 and 1990 pounds.
0.1254 or 12.54%
If 8% of all people in a certain geographic region are unemployed, find the probability that in a sample of 200 people, 20 are unemployed.
0.0604 or 6.04%
On the daily run of an express bus, the average number of passengers is 48. The standard deviation is 3. Assume the variable is normally distributed. Find the probability that the bus will between 43 and 47 passengers.
0.3232 or 32.32%