Suppose the weight of grizzly bears is normally distributed with a mean of 597.5 lbs and a standard deviation of 195 lbs. A male grizzly bear is randomly selected.

a. Find the probability that its weight is below 600 lbs.
b. Find the probability that its weight is between 550 lbs and 650 lbs.
c. Find the probability that its weight is more than 590 lbs.

The probabilities for the grizzly bear's weight can be calculated using concepts of mean, standard deviation, and z-score in a normal distribution. Given the mean and standard deviation, we can determine relative probabilities that a randomly selected bear's weight falls within certain ranges.

Explanation:

We can answer this question using the principles of statistics and standard deviation. Given a mean of 597.5lbs and a standard deviation of 195lbs for grizzly bear weight:

A.Probability the weight is below 600lbs: Since 600lbs is close to the mean, the probability would be around 0.5, or 50%.
B. Probability the weight is between 550lbs and 650lbs: Here, we want to calculate the number of standard deviations 550lbs and 650lbs are from the mean. We then use the z-score to find the cumulative probability.
C. Probability the weight is more than 590lbs: Similar to part B, we calculate the number of standard deviations 590lbs is away from the mean, use the z-score to find the cumulative probability, and subtract this from 1 (since we want to know the probability it is 'more than').

These concepts, namely the mean, standard deviation, and probabilities in a normal distribution, are crucial elements of statistics.

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