SET A
STATISTICS AND PROBABILITY
Name:
Grade & Section:
Direction: Calculate the mean, variance and standard deviation. Express your answers to the nearest thousandths.
1. A baker sells three types of bread: sourdough, rye, and wheat. The daily demand for each type of bread is a discrete
random variable. Let X represent the daily demand for sourdough loaves. The probability distribution of X is given by:
X
P(X) 𝑋 ∙ 𝑃(𝑋) (𝑋 − 𝜇) (𝑋 − 𝜇)2 (𝑋 − 𝜇)2 ∙ 𝑃(𝑋)
Mean: _____________
10
0.3
Variance: __________
15
0.4
20
0.4
Standard Deviation: __________
𝝁=
𝝈𝟐 𝒙 =
2. Consider a population consisting of 1, 2, 3, 4, and 6. Samples of size 3 are drawn from this population.
Sample Mean
(X)
f
P(X)
𝑋 ∙ 𝑃(𝑋)
𝑋−𝜇
(𝑋 − 𝜇)2
(𝑋 − 𝜇)2 ∙ 𝑃(𝑋)
Mean: _____________
Variance: __________
Standard Deviation: ______
T=
𝜇=
𝜎2𝑥 =
3. A teacher wants to estimate the average score on a recent exam. They randomly sample 25 students and find that their
average score is 78 points, with a sample standard deviation of 10 points. Construct a 90% confidence interval for the
population mean exam score.
4. A human resources manager wants to estimate the average salary of employees in a large company. They randomly sample
50 employees and find their average salary is $65,000 with a population standard deviation of $10,000. Construct a 95%
confidence interval for the population mean salary.
SET B
STATISTICS AND PROBABILITY
Name:
Grade & Section:
Direction: Calculate the mean, variance and standard deviation. Express your answers to the nearest thousandths.
1. A baker sells three types of bread: sourdough, rye, and wheat. The daily demand for each type of bread is a discrete
random variable. Let X represent the daily demand for sourdough loaves. The probability distribution of X is given by:
X
P(X) 𝑋 ∙ 𝑃(𝑋) (𝑋 − 𝜇) (𝑋 − 𝜇)2 (𝑋 − 𝜇)2 ∙ 𝑃(𝑋)
Mean: _____________
10
0.2
Variance: __________
15
0.3
20
0.5
Standard Deviation: __________
𝝁=
𝝈𝟐 𝒙 =
2. Consider a population consisting of 2, 3, 4, 5, and 6. Samples of size 3 are drawn from this population.
Sample Mean
(X)
f
P(X)
𝑋 ∙ 𝑃(𝑋)
𝑋−𝜇
(𝑋 − 𝜇)2
(𝑋 − 𝜇)2 ∙ 𝑃(𝑋)
Mean: _____________
Variance: __________
Standard Deviation: ______
T=
𝜇=
𝜎2𝑥 =
3. A teacher wants to estimate the average score on a recent exam. They randomly sample 35 students and find that their
average score is 80 points, with a sample standard deviation of 10 points. Construct a 95% confidence interval for the
population mean exam score.
4. A human resources manager wants to estimate the average salary of employees in a large company. They randomly sample
50 employees and find their average salary is $75,000 with a population standard deviation of $5,000. Construct a 99%
confidence interval for the population mean salary.