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b. what is the probability of generating a random number between and (to 1 decimal place)? .6 c. what is the probability of generating a random number with a value less than or equal to (to 1 decimal place)? d. what is the probability of generating a random number with a value greater than (to 1 decimal place)?

User Jamari
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Final answer:

With continuous random variables, we calculate the probability within a range rather than a specific value, and the probability of any single value is zero. P(x < c) and P(x ≤ c) are equivalent statements for continuous random variables. The probability that X is greater than a given value can be found by subtracting the probability of X being less than or equal to that value from 1. Therefore, the probability of X being greater than 5 is 0.65 or 65%.

Step-by-step explanation:

With continuous random variables, we never calculate the probability that X has a particular value, but we always speak in terms of the probability that X has a value within a particular range. This is because for a continuous random variable, the probability of any single value is zero. Instead, we calculate the probability that X falls within a specific range.

For a continuous random variable, P(x < c) and P(x ≤ c) are equivalent statements because the probability of any single value is zero. So, the probability that X is less than or equal to a specific value c is the same as the probability that X is strictly less than c.

If P(x < 5) = 0.35, then P(x > 5) is 1 - P(x < 5). In this case, P(x > 5) = 1 - 0.35 = 0.65. This is because the total probability of a continuous probability function is always 1. Therefore, the probability of X being greater than 5 is 0.65 or 65%.

User JesseW
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