International College of Digital Innovation, CMU
July 2, 2025
Question 1:
The height of adult males is normally distributed with a mean of 175 cm and a standard deviation of 8 cm. What is the probability that a randomly selected male is shorter than 180 cm?
Answer 1 \(P(X < 180)\) where \(X \sim N(175, 8^2)\)
Question 2:
The weight of apples in a farm follows a normal distribution with a mean of 150 grams and a standard deviation of 20 grams. What is the probability that an apple weighs more than 170 grams?
Answer 2 \(P(X > 170)\) where \(X \sim N(150, 20^2)\)
Question 3:
The lifetime of a light bulb is normally distributed with a mean of 1,000 hours and a standard deviation of 100 hours. What is the probability that a light bulb lasts between 900 and 1,100 hours?
Answer 3 \(P(900 < X < 1100)\) where \(X \sim N(1000, 100^2)\)
Question 4:
The scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 100. What score corresponds to the 95th percentile?
Answer 4 Find \(x\) such that: \(P(X < x) = 0.95\), where \(X \sim N(500, 100^2)\)
Question 5:
The delivery time of a shipping company follows a normal distribution with a mean of 3 days and a standard deviation of 0.5 days. What is the delivery time below which 80% of packages are delivered?
Answer 5 Find \(x\) such that: \(P(X < x) = 0.80\), where \(X \sim N(3, 0.5^2)\)
Question 6:
The temperature in a city during summer is normally distributed with a mean of 30°C and a standard deviation of 3°C. What is the probability that on a given day, the temperature is lower than 25°C?
Answer 6 \(P(X < 25)\) where \(X \sim N(30, 3^2)\)
Question 7:
A machine produces metal rods whose lengths follow a normal distribution with a mean of 50 cm and a standard deviation of 1.5 cm. Find the probability that a randomly selected rod is longer than 52 cm.
Answer 7 \(P(X > 52)\) where \(X \sim N(50, 1.5^2)\)
Question 8:
The exam scores for a class are normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that a student scores between 60 and 85?
Answer 8 \(P(60 < X < 85)\) where \(X \sim N(70, 10^2)\)
Question 9:
The daily sales of a shop are normally distributed with a mean of $5,000 and a standard deviation of $800. What sales value corresponds to the lowest 10% of sales?
Answer 9 Find \(x\) such that: \(P(X < x) = 0.10\), where \(X \sim N(5000, 800^2)\)
Question 10:
The body temperature of healthy adults is normally distributed with a mean of 98.6°F and a standard deviation of 0.7°F. What is the probability that a person has a temperature above 100°F?
Answer 10 \(P(X > 100)\) where \(X \sim N(98.6, 0.7^2)\)
Question 1:
A factory produces light bulbs with a defect rate of 5%. If 20 bulbs are selected at random, what is the probability that exactly 2 bulbs are defective?
Answer 1 Find \(P(X = 2)\), where \(X \sim Binomial(n = 20, p = 0.05)\)
Question 2:
A multiple-choice test has 10 questions, each with 4 choices and only one correct answer. If a student guesses on all questions, what is the probability that the student gets at least 7 correct answers?
Answer 2 Find \(P(X \geq 7)\), where \(X \sim Binomial(n = 10, p = 0.25)\)
Question 3:
In a quality control inspection, 15 items are tested. The probability of any item being defective is 10%. What is the probability that at most 3 items are defective?
Answer 3 Find \(P(X \leq 3)\), where \(X \sim Binomial(n = 15, p = 0.10)\)
Question 4:
A basketball player has a free throw success rate of 80%. What is the probability that he makes exactly 9 successful free throws out of 12 attempts?
Answer 4 Find \(P(X = 9)\), where \(X \sim Binomial(n = 12, p = 0.80)\)
Question 5:
A telemarketer calls 30 people, and the probability that any person answers is 20%. What is the probability that fewer than 5 people answer the call?
Answer 5 Find \(P(X < 5)\), where \(X \sim Binomial(n = 30, p = 0.20)\)
Question 6:
A call center receives an average of 6 calls per hour. What is the probability that exactly 8 calls are received in one hour?
Answer 6 Find \(P(X = 8)\), where \(X \sim Poisson(\lambda = 6)\)
Question 7:
A website experiences an average of 3 server crashes per month. What is the probability that there are no crashes in a particular month?
Answer 7 Find \(P(X = 0)\), where \(X \sim Poisson(\lambda = 3)\)
Question 8:
A hospital receives an average of 4 emergency patients per night. What is the probability that more than 5 emergency patients arrive tonight?
Answer 8 Find \(P(X > 5)\), where \(X \sim Poisson(\lambda = 4)\)
Question 9:
The number of car accidents at a busy intersection averages 2 per week. What is the probability that there are at most 1 accident next week?
Answer 9 Find \(P(X \leq 1)\), where \(X \sim Poisson(\lambda = 2)\)
Question 10:
An email system receives spam messages at an average rate of 10 per hour. What is the probability that exactly 15 spam messages arrive in one hour?
Answer 10 Find \(P(X = 15)\), where \(X \sim Poisson(\lambda = 10)\)
Question 1: What is the mean, median, and standard deviation of the variable Age?
Question 2: What is the minimum and maximum value of Income?
Question 3: What is the interquartile range (IQR) of Score?
Question 4: How many males and females are there in the dataset?
Question 5: What percentage of the sample is female?
Question 6: What is the range of Age?
Question 7: Create a histogram of the Income variable. What can you say about the distribution shape (symmetric, skewed)?
Question 8: Calculate the coefficient of variation (CV) for Score.
Question 9: What is the 75th percentile (Q3) of Income?
Question 10: Create a boxplot of Age. Are there any possible outliers?
Question 11: What is the mean and standard deviation of Income for males and females separately?
Question 12: What is the mean and standard deviation of Score for males and females separately?
Question 13: Compare the median Age between males and females. Which gender has a higher median age?
Question 14: What is the percentage of males and females who scored above 90?
Question 15: Create side-by-side boxplots of Income by gender. Comment on the spread and center of the distributions.
Question 16: Calculate the proportion of males and females whose Age is above 40.
Question 17: For each gender, what is the 25th percentile (Q1) and 75th percentile (Q3) of Score?
Question 18: Create side-by-side histograms of Age for males and females. Which gender shows more variability?
Question 19: Calculate the coefficient of variation (CV) for Income separately for males and females.
Question 20: Create a summary table showing count, mean, and standard deviation of Income and Score by gender.