Final answer:
To calculate the mean value of students who want a new copy of a textbook, you multiply the number of students (15) by the probability of wanting a new copy (0.3) to get 4.5. The standard deviation is found by taking the square root of the product of the number of students (15), the probability of success (0.3), and the probability of failure (0.7), resulting in approximately 1.7748.
Step-by-step explanation:
The question involves finding the mean and standard deviation for a binomial distribution, where each student who wants a new textbook represents a success. Since 30% of all students want a new book, the probability of success (p) is 0.3. The number of trials (n) is the number of purchasers, which is 15 in this scenario.
To find the mean of the binomial distribution, we use the formula:
Mean = n * p
Thus, the mean number of students wanting a new copy is:
Mean = 15 * 0.3 = 4.5
The standard deviation of a binomial distribution is calculated using the formula:
Standard Deviation = √(n * p * (1 - p))
So, the standard deviation is:
Standard Deviation = √(15 * 0.3 * (1 - 0.3)) = √(15 * 0.3 * 0.7) = √(3.15) ≈ 1.7748
Therefore, the mean value is 4.5 and the standard deviation is approximately 1.7748.