Normal Distributions
A normal distribution is ______-shaped and symmetric.
Bell
What does a z-score tell you?
How many standard deviations an observation is from the mean.
True or False: The total area under a normal curve is 1.
True
Fill in: The first step when solving a normal distribution application is to ______ the normal curve and desired area.
Draw
What does CLT stand for?
Central Limit Theorem
True or False: In a normal distribution, the mean, median, and mode are equal.
True
A student scores 85 on a test with μ = 80 and σ = 5. Find the z-score.
1
The standard normal table gives the area to the ______ of a z-score.
Left
If μ = 28 and σ = 2, what is the z-score for X = 30?
1
As sample size increases, the sampling distribution of the sample mean becomes more ______.
Normal
According to the Empirical Rule, approximately what percentage of observations fall within 2 standard deviations of the mean?
95%
A value has z = −2. What does the negative sign mean?
The value is 2 standard deviations below the mean.
Find P(Z > 2.11).
0.0174
If μ = 200 and σ = 20, what raw score corresponds to z = 1.285?
225.7
If σ = 18 and n = 36, find σₓ̄.
3
Fill in: Approximately ______% of observations in a normal distribution fall within 3 standard deviations of the mean.
99.7%
A test has μ = 76 and σ = 4. A student scores 85. Find z.
2.25
Find P(−1.50 < Z < 2.12).
0.9162
A newspaper has μ = 28 and σ = 2. Find P(27 < X < 31).
0.6247
A population has μ = 9.6, σ = 1.8, and n = 36. Find the z-score for x̄ = 9.
-2.00
A distribution has mean = median = mode, is symmetric and bell-shaped, and has one peak. What type of distribution is this?
Normal distribution
A student scores 72 on a test with μ = 80 and σ = 4. Find the z-score and interpret it.
z = −2; 2 SD below the mean
Find P(0.54 ≤ Z ≤ 2.33).
0.2847
Exam scores are normally distributed with μ = 200 and σ = 20. What score represents the top 10%?
Approximately 225.7
A population has μ = 96 months, σ = 16 months, and n = 36. Find P(90 < x̄ < 100).
0.921