A Bag Has 4 Types Of Coins: Two $1

Question

A bag has 4 types of coins as given below: • Two $1 • T 1. A bag has 4 types of coins as given below: Two $1 Three $5 One $10 Three $20 a. Construct a probability distribution table for the data. b. Calculate the variance. 2. One Market Research company determined that 13% of college students work part-time during the academic year. For a random sample of 5 students, what is the probability that at least 3 students work part-time? 3. Cream cheese is sold in cans that have a net weight of 8 ounces. The weights are normally distributed with a mean of 8.025 ounces and a standard deviation of 0.125 ounces. You take a sample of 36 cans. Compute the probability that the sample would have a mean 7.995 ounces or more. 4. Suppose you survey that a random sample of 150 people from one hospital has been given cholesterol tests, and 60 of these people had levels over the “safe” count of 200. Construct a 95% confidence interval for the population proportion of people in test with cholesterol levels over 200. 5. This is an observation from previous years about the impact of students working while they are enrolled in classes. Due to students working too much, they are spending less time on their classes. First, the observer needs to find out, on average, how many hours a week students are working. They know from previous studies that the standard deviation of this variable is about 5 hours. A survey of 200 students provides a sample mean of 7.10 hours worked. What is a 95% confidence interval based on this sample?

Dr. Jack HW Helper · Accepted Answer

To tackle the problems presented in the assignment, we will break down each question, perform necessary calculations, and discuss the statistical concepts involved. 1. Probability Distribution Table and Variance To construct the probability distribution table for the given coins, we first list out the counts of each type of coin: Value: $1, Count: 2 Value: $5, Count: 3 Value: $10, Count: 1 Value: $20, Count: 3 The total number of coins is 2 + 3 + 1 + 3 = 9. Now, the probability distribution table can be derived by dividing the count of each coin type by the total number of coins: Coin Value Count Probability $1 2 2/9 $5 3 3/9 $10 1 1/9 $20 3 3/9 Next, we calculate the variance: The expected value $ E(X) $ or mean of a discrete random variable is calculated as follows: Let $ X $ be the value of coins: $ 1, 5, 10, 20 $. Mean (µ) = $ E(X) = \sum (x \cdot P(x)) $ Calculating: $ E(X) = (1 \cdot \frac{2}{9}) + (5 \cdot \frac{3}{9}) + (10 \cdot \frac{1}{9}) + (20 \cdot \frac{3}{9}) = \frac{2 + 15 + 10 + 60}{9} = \frac{87}{9} = 9.67 $ To find variance, $ Var(X) = E(X^2) - (E(X))^2 $ Calculating $ E(X^2): $ $ E(X^2) = (1^2 \cdot \frac{2}{9}) + (5^2 \cdot \frac{3}{9}) + (10^2 \cdot \frac{1}{9}) + (20^2 \cdot \frac{3}{9}) $ = $ \frac{2 + 75 + 100 + 1200}{9} = \frac{1377}{9} \approx 153.00 $ So, the variance $ Var(X) = 153.00 - (9.67)^2 = 153.00 - 93.51 \approx 59.49 $. 2. Part-time Employment Probability Given that 13% of college students work part-time, we are to find the probability that at least 3 out of 5 randomly selected students work part-time. This follows a binomial distribution $ B(n=5, p=0.13) $. We need to calculate $ P(X \geq 3) = 1 - P(X Calculating those: For \( P(X=k) = \binom{n}{k} p^k (1-p)^{n-k} $. Calculating: - $ P(X=0) = \binom{5}{0} (0.13)^0 (0.87)^5 = 1 \cdot 1 \cdot 0.5132 \approx 0.5132 $ - $ P(X=1) = \binom{5}{1} (0.13)^1 (0.87)^4 = 5 \cdot 0.13 \cdot 0.5997 \approx 0.3894 $ - \( P(X=2) = \binom{5}{2} (0.13)^2 (0.87)^3 = 1

A Bag Has 4 Types Of Coins: Two $1 ✓ Solved

A bag has 4 types of coins as given below: • Two $1 • T

Paper For Above Instructions

1. Probability Distribution Table and Variance

2. Part-time Employment Probability

3. Sample Mean Probability

4. Confidence Interval for Cholesterol Level

5. Confidence Interval for Work Hours

Conclusion

References