Question

Consider the following data: x 4 5 6 7 8 P(X=x) 0.2 0.2 0.1 0.2 0.3

Step 2 of 5: Find the variance. Round your answer to one decimal place.
Step 3 of 5: Find the standard deviation. Round your answer to one decimal place.
Step 4 of 5: Find the value of P(X<7). Round your answer to one decimal place
Step 5 of 5:Find the value of P(X≥7). Round your answer to one decimal place.

Answer 1

The random variable X represents the number of books checked out by a patron. The variance is 4.9 and the standard deviation is 2.2. The probability that X is less than 7 is 0.7 and the probability that X is greater than or equal to 7 is 0.3.

Step-by-step explanation:

The random variable X for this example represents the number of books checked out by a patron.

The variance can be found by using the formula: variance = Σ(x - mean)² * P(x). Calculating each term and summing them up, we get variance = 1.156 + 1.2 + 0.144 + 1.352 = 4.852. So, the variance is 4.9 (rounded to one decimal place).

The standard deviation can be found by taking the square root of the variance. So, the standard deviation is √4.9 ≈ 2.2 (rounded to one decimal place).

P(X<7) can be found by adding up the probabilities of all values less than 7. P(X<7) = 0.2 + 0.2 + 0.1 + 0.2 = 0.7 (rounded to one decimal place).

P(X≥7) can be found by subtracting P(X<7) from 1. So, P(X≥7) = 1 - 0.7 = 0.3 (rounded to one decimal place).