Questions: d. P(z ≥ -2.5) e. P(-3 < z ≤ 0)

Question

Questions: d. P(z ≥ -2.5) e. P(-3 < z ≤ 0)

Transcript text: d. $P(z \geq-2.5)$ e. $P(-3

Solution

Solution Steps

Step 1: Calculate $ P(z \geq -2.5) $

To find the probability $ P(z \geq -2.5) $, we can express it using the cumulative distribution function $ \Phi $:

\[ P(z \geq -2.5) = 1 - P(z < -2.5) = 1 - \Phi(-2.5) \]

Using the properties of the standard normal distribution, we have:

\[ P(z \geq -2.5) = \Phi(\infty) - \Phi(-2.5) = 0.9938 \]

Thus, the result for part d is:

\[ \boxed{P(z \geq -2.5) = 0.9938} \]

Step 2: Calculate $ P(-3 < z \leq 0) $

To find the probability $ P(-3 < z \leq 0) $, we can express it as:

\[ P(-3 < z \leq 0) = P(z \leq 0) - P(z \leq -3) = \Phi(0) - \Phi(-3) \]

Using the cumulative distribution function values, we have:

\[ P(-3 < z \leq 0) = \Phi(0) - \Phi(-3) = 0.4987 \]

Thus, the result for part e is:

\[ \boxed{P(-3 < z \leq 0) = 0.4987} \]

Final Answer

The answers to the questions are:

For part d: $ \boxed{P(z \geq -2.5) = 0.9938} $
For part e: $ \boxed{P(-3 < z \leq 0) = 0.4987} $

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Fifty-four wild bears were anesthetized, and then their weights and chest sizes were measured and listed in a data set. Results are shown in the accompanying display. Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes? When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that a measured chest size can be used to predict the weight? Use a significance level of α=0.05. Determine the null and alternative hypotheses. H0: p=□ H1: ρ> Identify the correlation coefficient, r. r= □ Identify the critical value(s). A. There are two critical values at r= ± □ B. There is one critical value at r= □ Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes? Choose the correct answer below and, if necessary, fill in the answer box within your choice. A. Yes, because the correlation coefficient □ falls outside the critical value(s). B. No, because the correlation coefficient □ falls outside the critical value(s). C. No, because the correlation coefficient □ falls between the critical values. D. Yes, because the correlation coefficient □ falls between the critical values. E. The answer cannot be determined from the given information. When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that a measured chest size can be used to predict the weight? A. Yes, it is easier to measure a chest size than a weight because measuring weight would require lifting the bear onto the scale. The chest size could not be used to predict weight because there is not a linear correlation between the two. B. Yes, it is easier to measure a chest size than a weight because measuring weight would require lifting the bear onto the scale. The chest size could be used to predict weight because there is a linear correlation between the two. C. No, it is easier to measure weight than chest size because the chest is not a flat surface. D. Yes, it is easier to measure a chest size than a weight because measuring weight would require lifting the bear onto the scale. The chest size could not be used to predict weight because there is too much variance in the weight of the bears.

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