Empirical Rule
The percentage of values that fall below z=-1
16%
Fish in trout creek have lengths that are normally distributed with a mean 45 in and standard deviation 5.2 in. Find the probability of a randomly selected trout being less than 36 inches.
4.17%
The trout in Lander's pond are normally distributed with a mean 12 lbs. and standard deviation 4 lbs. If random samples of 35 trout are selected, what is the standard deviation of the sampling distribution of x-bar?
0.6761 lbs.
20% of all m&m candies are orange. What is the standard deviation of the sampling distribution of samples of 100 m&ms?
.04
This z-score is greater than 30% of the values on a standard normal curve.
z=-.524
The proportion of values fall between z=-2 and z=2
95%
SAT scores are normally distributed with mean 520 and standard deviation 40. Find the probability a randomly selected student scores between a 500 and 620.
68.53%
The trout in Lander's pond are normally distributed with a mean 12 lbs. and standard deviation 4 lbs. If random samples of 35 trout are selected, what is the probability that a sample has an average weight below 10 lbs.?
0.15%
If 20% of all m&m candies are orange, find the probability that a sample of 100 candies has fewer than 12 orange m&ms.
2.28%
What z-score represents the top 20% of a standard normal distribution?
0.84
The percentage of values that fall above z = -2
97.5%
The number of m&ms dispensed by a machine is normally distributed with mean 15 m&ms and standard deviation 2 m&ms. Find the probability a machine dispenses less than 10 m&ms.
0.62%
The trout in Lander's pond are normally distributed with a mean 12 lbs. and standard deviation 4 lbs. If random samples of 35 trout are selected, what is the probability that a sample has an average weight between 11.5 and 12.2 lbs.
38.65%
56% of all students take AP classes their junior year. Find the probability that a randomly selected sample of 30 juniors has more than 70% taking AP classes.
6.12%
Math SAT scores are normally distributed with mean 570 and standard deviation 40. What score represents the lowest possible score in the top 10%?
622
The proportion of values that fall between z=-3 and z=2
97.35%
The number of students late to school are normally distributed with a mean of 42 and standard deviation 7. What is the probability that more than 55 students are late on a randomly selected day?
3.16%
The weekly salaries of teachers in one state are normally distributed with mean $550 and standard deviation $60. What is the probability that an SRS of 50 teachers from that state have a mean salary above $570 per week?
0.92%
72% of teens use social media during school. SRSs size 48 are taken from HS students. What is the probability that fewer than 30 of them use social media during school?
7.13%
Americans expenditures on Valentine's Day are normally distributed with mean $100 and standard deviation $20. What dollar amount represents the bottom 15% of spenders? (Round to the nearest cent)
$79.27
P(z<-2) or P(z>1)
18.5%
Dogs weights are normally distributed with a mean 72 lbs. and standard deviation 5 lbs. What is the probability a randomly selected dog weighs less than 64 lbs. or more than 80 lbs.?
10.96%
The weekly salaries of teachers in one state are normally distributed with mean $550 and standard deviation $60. What is the probability that an SRS of 50 teachers from that state have a mean salary between $520 - $540?
11.9%
80% of Americans wear their seatbelts regularly. Find the probability that between 85% and 90% of a sample of 50 Americans wear their seatbelts regularly.
14.98%
Mr. Smith fails the bottom 5% of his class. If the class average is 77% with standard deviation 6%, find the highest grade in his class that will receive a failing grade if decimal grades are not possible.
67%