Intro To Normal Distribution & Standard Normal Distribution
Normal Distributions :
Finding Probablilities
Finding Probablilities
Z ain't just for zombies!
Sampling Distributions & The Central Limit Theorem
Sampling Dist. of Proportions
100
With a bell-shaped, symmetric curve, _____ % of the data lie within one standard deviation of the mean.
What is 68?
100
Complete the sentence.
A normal Distribution has _______________ shape and is ______________ about the middle and most frequent value known as ________________?
"A normal Distribution has A BELL shape and is SYMMETRIC about the middle and most frequent value known as THE MEAN?
100
What's your favorite class?
That's E-Z!
What is Statistical Reasoning?
:D
100
What Is The Standard Deviation Of The Sample Mean Equal To ?
What is Equal To The Population Standard Deviation
100
If the probability of success is p, the probability of NOT success is. . .?
What is 1-p = q?
200
With a bell-shaped, symmetric curve, _____ % of the data lie within two standard deviations of the mean.
What is 95%
200
What is the formula used to find your z-score for a normal distribution in words?
z = (x-mu)/(sigma)
200
How do you transform A Standard z-Score To A Data Value x In A Given Population ?
If
z=(x-mu)/sigma
then
x = (z)(sigma)+mu
200
What is the formula for the standard deviation related to a sampling distribution of a quantitative variable?
sigma_bar(x)=sigma/sqrt(n)
200
a census was conducted and found that 12,000 residents said yes to a question. If there are 13,500 in the population, find mu_p .
The proportion is 12,000/13,500 = .bar(88) .
300
About ____-% of the data of the data lie within 3 standard deviations of the mean.
What is 99.7%
300
A variable of interest has a mean of 12.5 and a standard deviation of 2.5. Find the z-score for a value of 13
What is z = 0.2
300
What z-score would be associated with a probability close to 1.00?
What is 3.49 or 3.5?
300
The mean ACT composite score in recent year is 20.8 A random sample of 36 ACT composite scores is selected from the population. What is the probability that the mean score is more than 19.8 , assuming the standard deviation is 5.6?
What is 0.8577?
300
72% of residents in a town lock their doors at night. A recent survey of 1500 residents was conducted. Find the standard deviation?
sigma = sqrt(((.72)(.28))/1500) approx .0116
400
What is the name of the rule that specifics that for a normal distribution, almost all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ)
What is Empirical Rule?
400
What is the probability or area associated with a z-score of 0.34?
What is 0.6331?
400
What is the area under the standard normal curve to the right of z = 0.015?
What is 0.4940?
400
The mean ACT composite score in recent year is 20.8 A random sample of 36 ACT composite scores is selected from the population. What is the probability that the mean score is less than 21.6, assuming the standard deviation is 5.6?
What is
0.8051?
400
A population has a proportion value of 37% for some characteristic. A sample of 49 residents was conducted, find the probability the sample proportion is less than 35%
What is .3859?
500
The apples at an orchard are normally distributed with a mean weight of 7 grams and a standard deviation of 1.5 grams.
• Complete the sentence. 68% of all apple weights are between ________ grams and _________ grams.
What is 68% of all apple weights are between 5.5 grams and 8.5 grams?
500
A normal distribution has a mean of 6.7 and a standard deviation of 1.67. Find the probability of a randomly selected outcome between 6 & 7?
What is 0.5714 - 0.3372 = 0.2342?
500
calculate the standard deviation for the data set by hand:
{4, 3, 6, 5, 5, 7}
500
A distribution of means has an average of 32.7 and a standard deviation of 10. What is the probability that a sample of 144 individuals has a mean of 34 or less?
What is .9406?
500
A recent study showed that 75% of adults believe that math has made the world a better place. A local university student polled 100 random people. Find the probability his results show between 72% and 77% hold this same opinion. (Find sigma_hat(p) to four decimal places)
Our z-scores are 0.46 and -0.69 which gives respective probabilities which we can subtract to find the answer which is .6772 - .2451 = .4321.