Solving for Z-scores
Elias collected 85 candies on Halloween. If trick-or-treaters collect an average of 72 candies with a standard deviation of 5, what is Elias' z-score?
z = 2.6
Corina throws a costume party each year for Halloween. On average, 70 people attend her parties with a standard deviation of 20. What is the probability that less than 90 people will attend Corina's party?
P(x<90) = .8413
David got a 22 for his ACT score, and the average ACT score in the United States is 20 with a standard deviation of 4. Marisa got a 1400 for her SAT score, and the average SAT in the United states is 1000 with a standard deviation of 200. Who did better on their test?
Marisa
Symmetric, bell curve distribution typically used to find probabilities and z-scores.
Standard Normal Z-Distribution
If a normal distribution has mean of 32 and a standard deviation of 5, what value lies two standard deviations above the mean?
42
Throughout the month of October, Fresno residents watch Halloween movies an average of 3 times each week with a standard deviation of 1. Anthony watched 2 Halloween movies this week. Calculate his Z-score.
z = -1
Corina throws a costume party each year for Halloween. On average, 70 people attend her parties with a standard deviation of 20. What is the probability that less than 25 people will attend Corina's party?
P(x<25) = .0122
Bobbing for apples is an hold Halloween tradition. The Halloween party in Fresno bobbed an average of 7 apples with a standard deviation of 2. The party in Clovis bobbed an average of 6 apples with a standard deviation of 4. If Jamaal bobbed 12 apples at Fresno party and Will bobbed 12 apples at the Clovis party, who performed better?
Jamaal
This statistic indicates how particular values are scattered around the mean in a distribution.
Standard deviation
If a normal distribution has a mean of 18 and a standard deviation of 3, what value lies three standard deviations below the mean?
9
An average of 120 people visit the local pumpkin patch each day, with a standard deviation of 90. If 100 people watch scary movies, what is the corresponding z-score?
z = -0.22
Corina throws a costume party each year for Halloween. On average, 70 people attend her parties with a standard deviation of 20. What is the probability that more than 80 people will attend Corina's party?
P(x>80) = .3085
Thousands of Americans visit their local pumpkin patch during the Halloween season. Planet Pumpkin has a mean of 100 people visit the patch per day with a standard deviation of 25. Cool Patch Pumpkins has an average of 70 people visit the patch per day with a standard deviation of 12. If Planet Pumpkin had a total of 120 visits and Cool Patch Pumpkins had a total of 84 visits, which pumpkin patch had the best turnout?
Cool Patch Pumpkins
This allows us to compare different units on equal grounds
Z-score
A normal distribution has a mean of 50 and a standard deviation of 25. 125 lies three standard deviations above the mean. What is the corresponding z-score?
z = 3
A normal distribution of people's favorite Halloween movies has a mean of 0 and a standard deviation of 5. Find the z-score corresponding to a value 15 points above the mean.
z = 3
Corina throws a costume party each year for Halloween. On average, 70 people attend her parties with a standard deviation of 20. What is the range that 95% of people will attend Corina's party?
range = 30.8 or 31-109 people
In Fresno, trick-or-treaters collected an average of 35 candies with a standard deviation of 7. In Madera, trick-or-treaters collected an average of 33 candies with a standard deviation of 4. If Anthony collected 44 candies in Fresno and Inez collected 40 in Madera, who was the more successful trick-or-treater?
Inez
The number of scores in a sample that reflect the random variability in a population
Degrees of Freedom
The equation z = -1.33 indicates that a particular value lies:
1.33 standard deviations below the mean
Families carve an average of 4 pumpkins for Halloween with a standard deviation of 2. Find the corresponding z-scores for the following values:
a. 8
b. 2
c. 5
a. 2
b. -1
c. 0.5
What value represents the 50th percentile of Corina's data set? (μ = 70, σ = 20)
Hint: use the reverse z-score formula x = z(σ) + μ
50th percentile = 0.50
Search for the probability closest to 0.50 on the z-table and find its corresponding z-score
Plug the values into the reverse z-score formula:
x = 0(20) + 70
x = 70
George and Angie throw Halloween parties every year. Data from previous years show an average 44 people go to George's party with a standard deviation of 12, and an average of 52 people go to Angie's party with a standard deviation of 18. If 55 people go to George's party and 65 people go to Angie's party this year, whose party had the best turnout?
George
This table contains positive and negative z-scores and their corresponding probabilities.
Z-table
The equation z = 3.56 indicates that a particular value lies:
3.56 standard deviations above the mean