Question

The weights of Maine lobsters at the time of their catch are normally distributed with a mean of 1.8lb and a standard deviation of 0.25lb. What is the probability that a randomly selected lobster weighs (a) between 1.5 and 2lb ?, (b) more than 1.55lb?, (c) less than 2.2lb ? 4. The postsurgery survival time of a breast cancer patient is normally distributed with a mean of eight years and a standard deviation of 1.5 years. Find the probabilities that a woman with breast cancer will survive after her surgery: (a) between five and seven years, (b) more than 11 years, (c) less than six years.

Answer 1

To find probabilities for the weight of Maine lobsters, we can use z-scores and the standard normal distribution. We can calculate the probabilities for the given weight ranges using the z-table.

Step-by-step explanation:

To find the probability, we need to use the standard normal distribution. We can convert the given values into z-scores using the formula: z = (x - mean) / standard deviation.

(a) To find the probability that a randomly selected lobster weighs between 1.5 and 2 lb, we calculate the z-scores for both weights and use the z-table to find the probabilities. P(1.5 < x < 2) = P(z < (2 - 1.8) / 0.25) - P(z < (1.5 - 1.8) / 0.25).

(b) To find the probability that a randomly selected lobster weighs more than 1.55 lb, we calculate the z-score for 1.55 lb and use the z-table to find the probability. P(x > 1.55) = 1 - P(z < (1.55 - 1.8) / 0.25).

(c) To find the probability that a randomly selected lobster weighs less than 2.2 lb, we calculate the z-score for 2.2 lb and use the z-table to find the probability. P(x < 2.2) = P(z < (2.2 - 1.8) / 0.25).