A card is drawn from a standard 52-card deck. P(King) = 4/52 and P(Heart) = 13/52 and P(King of Hearts) = 1/52. What is P(King OR Heart)?
Which of the following are required conditions for a Binomial distribution? Select ALL that apply.
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Fill in the R function to find P(X = 4) when X ~ Binomial(n=10, p=0.3):
_____(4, size = 10, prob = 0.3)X ~ Binomial(12, 0.4). What R code gives P(X ≥ 5)?
X ~ Binomial(20, 0.3). Which statements are TRUE? Select ALL that apply.
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P(A) = 0.6 and P(B) = 0.5. If A and B are INDEPENDENT, what is P(A ∩ B)?
Events A and B are MUTUALLY EXCLUSIVE with P(A) > 0 and P(B) > 0. Which statements are TRUE? Select ALL that apply.
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X ~ N(75, 100) (mean=75, variance=100, so sd=10). Fill in the R function to find P(X ≤ 88):
_____(88, mean = 75, sd = 10)X ~ N(100, 225) (mean=100, sd=15). Which statements follow from the 68-95-99.7 rule? Select ALL that apply.
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Exam scores are normally distributed with mean 72 and sd 8. A student scores 88. What is their z-score?
X ~ N(72, 64) (mean=72, sd=8). Fill in the R function to find the score at the 90th percentile:
_____(0.90, mean = 72, sd = 8)A population has mean μ = 50 and sd σ = 20. We take random samples of size n = 100. Which statements about the sampling distribution of x are TRUE? Select ALL that apply.
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Which R function would you use to find P(X = 7) for X ~ Binomial(15, 0.45)?
# Which function gives the EXACT probability at a single value?P(A) = 0.4, P(B) = 0.3, P(A ∩ B) = 0.12. Which statements are TRUE? Select ALL that apply.
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X ~ N(68, 100) (mean=68, sd=10). What R code gives P(X > 75)?
If P(A) = 0.3, what is P(A')?
P(A) = 0.4, P(B) = 0.5, P(A and B) = 0.2. What is P(A or B)?
A and B are independent, P(A)=0.3, P(B)=0.4. What is P(A and B)?
P(A and B) = 0.15, P(B) = 0.5. What is P(A|B)?
Which condition makes two events mutually exclusive?
A fair die is rolled. What is P(rolling a prime: 2, 3, or 5)?
Knowing B occurred doesn't change P(A). What does this mean?
Can two events with positive probability be both mutually exclusive AND independent?
Bayes' theorem is most useful for:
Two events have P(A)=0.6, P(B)=0.3, and they are mutually exclusive. What is P(A or B)?
What does dbinom(5, 10, 0.5) compute?
X ~ Binomial(15, 0.4). What is E[X]?
How would you compute P(X >= 3) for X ~ Binomial(8, 0.25)?
A fair coin is flipped 10 times. What is Var(X) where X = number of heads?
Which is NOT a required condition for the Binomial distribution?
What does pbinom(4, 10, 0.3) return?
X ~ Binomial(12, 0.5). What is the standard deviation?
A student guesses randomly on 10 true/false questions. What is P(exactly 8 correct)?
As p approaches 0.5, the binomial distribution shape becomes:
What does C(n,k) in the Binomial PMF count?
For X ~ N(50, 9) (mean=50, variance=9), what is the standard deviation?
What does pnorm(1.96) (default mean=0, sd=1) approximately return?
Heights ~ N(68, 9). About what % of people are between 65 and 71 inches?
A student scores 85 on a test with mean 75 and SD 10. What is their z-score?
How would you compute the 95th percentile of N(100, 225) in R? (variance=225, so sd=15)
What does the Central Limit Theorem say about sample means?
How do you compute P(X > 90) for X ~ N(80, 100) in R?
As sample size n increases, what happens to the standard error SE = sigma/sqrt(n)?
For a standard normal distribution, approximately what percent of values fall below z = -2?
The normal distribution can be used to make inferences about non-normal populations when n is large, because of:
A 95% CI for mu is (12.3, 18.7). Which interpretation is correct?
What happens to CI width as sample size n increases?
You get a p-value of 0.03 with alpha = 0.05. What is your conclusion?
What is a Type I error?
In R, t.test(x, mu = 10) tests:
Why use t-distribution instead of normal for most t-tests?
A 99% CI will be ______ than a 95% CI from the same data.
In a one-sided test with Ha: mu > 70, the p-value includes:
Which df gives heavier tails, qt(0.975, df=5) or qt(0.975, df=30)?
A result is statistically significant (p < 0.05) but has a very small effect size. This means:
In a two-group proportion study, H0: p1 = p2. For the hypothesis test SE, should you use pooled or individual proportions?
SE of p-hat when p-hat = 0.6, n = 100?
For a 95% CI for a proportion, which z* value?
For two proportions, if the 95% CI for (p1 - p2) is (-0.05, 0.15), what can you conclude?
When comparing two proportions, why use the pooled proportion in the hypothesis test but individual proportions for the CI?
For the normal approximation to be valid for proportions, which condition must hold?
A 95% CI for p is (0.501, 0.599). What can you conclude about H0: p = 0.5?
Chimp study: with partner 60/90, without partner 16/30. Pooled proportion p-pool =?
Using p = 0.5 for sample size planning when p is unknown gives:
You need a 95% CI with margin of error <= 0.03, no prior estimate of p. Approximately what n is needed?