Let x be a random variable that represents white blood cell count per cubic milliliter of whole blobd. Asst estimated standard deviation a = 2450. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection. n USE SALT (a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.) (b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? The probability distribution of x is approximately normal with = 7650 and o = 2450. O The probability distribution of x is not normal. O The probability distribution of x is approximately normal with u, = 7650 and os = 1732.41. O The probability distribution of x is approximately normal with G = 7650 and o, = 1225.00. What is the probability of x< 3500? (Round your answer to four decimal places.) (c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.) (d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased? The probabilities stayed the same as n increased. O The probabilities increased as n increased. The probabilities decreased as n increased.
Let x be a random variable that represents white blood cell count per cubic milliliter of whole blobd. Asst estimated standard deviation a = 2450. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection. n USE SALT (a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.) (b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? The probability distribution of x is approximately normal with = 7650 and o = 2450. O The probability distribution of x is not normal. O The probability distribution of x is approximately normal with u, = 7650 and os = 1732.41. O The probability distribution of x is approximately normal with G = 7650 and o, = 1225.00. What is the probability of x< 3500? (Round your answer to four decimal places.) (c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.) (d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased? The probabilities stayed the same as n increased. O The probabilities increased as n increased. The probabilities decreased as n increased.
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![### Understanding the Probability Distribution of White Blood Cell Count
**Problem Statement:**
Let \( x \) be a random variable that represents the white blood cell count per cubic milliliter of whole blood. Assume that \( x \) has a distribution that is approximately normal, with mean \( \mu = 7650 \) and estimated standard deviation \( \sigma = 2450 \). A test result of \( x \leq 3500 \) is an indication of leukopenia. This indicates bone marrow depression that may be the result of a vital infection.
**Questions:**
#### (a) What is the probability that, on a single test, \( x \) is less than 3500? (Round your answer to four decimal places.)
\[ P(x < 3500) = \_\_\_\_ \]
#### (b) Suppose a doctor uses the average \( \overline{x} \) for two tests taken about a week apart. What can we say about the probability distribution of \( x \)?
- The probability distribution of \( x \) is approximately normal with \( \mu_{\overline{x}} = 7650 \) and \( \sigma_{\overline{x}} = 2450 \)
- The probability distribution of \( \overline{x} \) is not normal.
- The probability distribution of \( \overline{x} \) is approximately normal with \( \mu_{\overline{x}} = 7650 \) and \( \sigma_{\overline{x}} = 1732.41 \)
- The probability distribution of \( \overline{x} \) is approximately normal with \( \mu_{\overline{x}} = 7650 \) and \( \sigma_{\overline{x}} = 1225.00 \)
(The correct answer is marked with a dot.)
#### What is the probability of \( \overline{x} < 3500 \)? (Round your answer to four decimal places.)
\[ P(\overline{x} < 3500) = \_\_\_\_ \]
#### (c) Repeat part (b) for \( n = 3 \) tests taken a week apart. (Round your answer to four decimal places.)
\[ P(\overline{x} < 3500) \text{ for } n = 3 = \_\_\_\_ \]
#### (d) Compare your answers to parts (a), (b), and (](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1da81aa5-c0e9-4d6e-87eb-a5febb367169%2Fa31690aa-b873-4e3d-9fe8-33e37b78e28f%2Fmy2x2l6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding the Probability Distribution of White Blood Cell Count
**Problem Statement:**
Let \( x \) be a random variable that represents the white blood cell count per cubic milliliter of whole blood. Assume that \( x \) has a distribution that is approximately normal, with mean \( \mu = 7650 \) and estimated standard deviation \( \sigma = 2450 \). A test result of \( x \leq 3500 \) is an indication of leukopenia. This indicates bone marrow depression that may be the result of a vital infection.
**Questions:**
#### (a) What is the probability that, on a single test, \( x \) is less than 3500? (Round your answer to four decimal places.)
\[ P(x < 3500) = \_\_\_\_ \]
#### (b) Suppose a doctor uses the average \( \overline{x} \) for two tests taken about a week apart. What can we say about the probability distribution of \( x \)?
- The probability distribution of \( x \) is approximately normal with \( \mu_{\overline{x}} = 7650 \) and \( \sigma_{\overline{x}} = 2450 \)
- The probability distribution of \( \overline{x} \) is not normal.
- The probability distribution of \( \overline{x} \) is approximately normal with \( \mu_{\overline{x}} = 7650 \) and \( \sigma_{\overline{x}} = 1732.41 \)
- The probability distribution of \( \overline{x} \) is approximately normal with \( \mu_{\overline{x}} = 7650 \) and \( \sigma_{\overline{x}} = 1225.00 \)
(The correct answer is marked with a dot.)
#### What is the probability of \( \overline{x} < 3500 \)? (Round your answer to four decimal places.)
\[ P(\overline{x} < 3500) = \_\_\_\_ \]
#### (c) Repeat part (b) for \( n = 3 \) tests taken a week apart. (Round your answer to four decimal places.)
\[ P(\overline{x} < 3500) \text{ for } n = 3 = \_\_\_\_ \]
#### (d) Compare your answers to parts (a), (b), and (
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