Final answer:
To find the probability that Mrs. Plum's cats will wake her up no more than five times next week, we can use the exponential distribution. The probability is calculated using the formula P(X <= 5) = 1 - e^(-0.1 * 5). The correct answer is option b. 0.3935.
Step-by-step explanation:
To find the probability that Mrs. Plum's cats will wake her up no more than five times next week, we need to use the exponential distribution. Since the average number of times her cats wake her up is ten per week, we can use this information to calculate the parameter lambda for the exponential distribution. The parameter lambda is equal to the reciprocal of the average, so lambda = 1/10 = 0.1.
The probability that her cats will wake her up no more than five times next week can be calculated as:
P(X <= 5) = 1 - e^(-0.1 * 5) = 1 - e^(-0.5) = 1 - 0.6065 = 0.3935
Therefore, the correct answer is option b. 0.3935