Suppose that samples of size n = 25 are selected at random from a normal population with mean 100 and standard deviation 10. What is the probability that the sample mean falls in the interval from μ-1.86x to μx + 1.40x? Express your answer to four decimal places (e.g. 0.9876). The probability is i 0.8054 Statistical Tables and Chart

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**Sample Mean Probability in a Normal Population**

Suppose that samples of size \( n = 25 \) are selected at random from a normal population with a mean of 100 and a standard deviation of 10. What is the probability that the sample mean falls in the interval from 
\[ \mu_X - 1.8\sigma_X \text{ to } \mu_X + 1.4\sigma_X? \]

Express your answer to four decimal places (e.g., 0.9876).

- ** The probability is**: \( \boxed{0.8054} \)
Transcribed Image Text:**Sample Mean Probability in a Normal Population** Suppose that samples of size \( n = 25 \) are selected at random from a normal population with a mean of 100 and a standard deviation of 10. What is the probability that the sample mean falls in the interval from \[ \mu_X - 1.8\sigma_X \text{ to } \mu_X + 1.4\sigma_X? \] Express your answer to four decimal places (e.g., 0.9876). - ** The probability is**: \( \boxed{0.8054} \)
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