document.write( "Question 1177034: Find the probability that a sample size of n=225 is randomly selected with a mean less than 244.3 \n" ); document.write( "
Algebra.Com's Answer #850536 by CPhill(2189)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "**Understanding the Problem**\r
\n" ); document.write( "\n" ); document.write( "* **Sample size (n):** 225
\n" ); document.write( "* **Sample mean (x̄):** 244.3
\n" ); document.write( "* **Population mean (μ):** 245 (This is the mean we're comparing to)
\n" ); document.write( "* **Population standard deviation (σ):** 15 (This is the standard deviation of the population)
\n" ); document.write( "* **We want to find:** P(x̄ < 244.3)\r
\n" ); document.write( "\n" ); document.write( "**Steps to Solve**\r
\n" ); document.write( "\n" ); document.write( "1. **Calculate the standard error of the mean (SE):**
\n" ); document.write( " SE = σ / √n
\n" ); document.write( " SE = 15 / √225
\n" ); document.write( " SE = 15 / 15
\n" ); document.write( " SE = 1\r
\n" ); document.write( "\n" ); document.write( "2. **Calculate the z-score:**
\n" ); document.write( " z = (x̄ - μ) / SE
\n" ); document.write( " z = (244.3 - 245) / 1
\n" ); document.write( " z = -0.7\r
\n" ); document.write( "\n" ); document.write( "3. **Find the probability (P-value):**
\n" ); document.write( " We want to find P(z < -0.7). This is the area under the standard normal distribution curve to the left of z = -0.7.
\n" ); document.write( " Using a z-table or calculator, we find that P(z < -0.7) ≈ 0.2420.\r
\n" ); document.write( "\n" ); document.write( "**Answer**\r
\n" ); document.write( "\n" ); document.write( "The probability that a sample size of 225 is randomly selected with a mean less than 244.3 is approximately 0.2420.
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