document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193276>Question 1193276</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The distribution of weekly salaries at a large company is right-skewed with a mean of RM1000 and a standard deviation of RM350. What is the probability in estimating the mean weekly salary for all employees of the company will be<BR>\n" );
document.write( "a)	Between RM900 and RM1100?<BR>\n" );
document.write( "b)	Below RM900?<BR>\n" );
document.write( "c)	Greater than RM850?<BR>\n" );
document.write( "d)	Exactly RM1000?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848849 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848849\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Understand the Central Limit Theorem**\r<BR>\n" );
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document.write( "* Even though the population of weekly salaries is right-skewed, the Central Limit Theorem states that the distribution of sample means will approach a normal distribution as the sample size increases. \r<BR>\n" );
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document.write( "* **Key Assumptions:**<BR>\n" );
document.write( "    * The sample size is sufficiently large (often considered 30 or more).<BR>\n" );
document.write( "    * The samples are drawn independently and randomly from the population.\r<BR>\n" );
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document.write( "**2. Calculate the Standard Error of the Mean**\r<BR>\n" );
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document.write( "* Standard Error (SE) = σ / √n <BR>\n" );
document.write( "    * Where σ is the population standard deviation <BR>\n" );
document.write( "    * And n is the sample size \r<BR>\n" );
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document.write( "**3. Calculate Z-scores**\r<BR>\n" );
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document.write( "* To find probabilities related to the sample mean, we need to standardize the values using the z-score formula:<BR>\n" );
document.write( "    * z = (x̄ - μ) / SE <BR>\n" );
document.write( "        * Where x̄ is the sample mean<BR>\n" );
document.write( "        * μ is the population mean<BR>\n" );
document.write( "        * SE is the standard error\r<BR>\n" );
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document.write( "**4. Find Probabilities**\r<BR>\n" );
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document.write( "* Use a standard normal distribution table or a calculator to find the probabilities associated with the calculated z-scores.\r<BR>\n" );
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document.write( "**Important Note:** \r<BR>\n" );
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document.write( "* Since the sample size (n) is not given in the problem, we cannot calculate the exact standard error and z-scores. <BR>\n" );
document.write( "* Therefore, we cannot provide specific numerical probabilities for parts (a) to (c).\r<BR>\n" );
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document.write( "**However, we can explain the general approach:**\r<BR>\n" );
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document.write( "**a) Between RM900 and RM1100**\r<BR>\n" );
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document.write( "* Calculate the z-scores for RM900 and RM1100 using the formula above.<BR>\n" );
document.write( "* Find the area under the standard normal curve between these two z-scores. This will give you the probability that the sample mean falls between RM900 and RM1100.\r<BR>\n" );
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document.write( "**b) Below RM900**\r<BR>\n" );
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document.write( "* Calculate the z-score for RM900.<BR>\n" );
document.write( "* Find the area under the standard normal curve to the left of this z-score. This will give you the probability that the sample mean is below RM900.\r<BR>\n" );
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document.write( "**c) Greater than RM850**\r<BR>\n" );
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document.write( "* Calculate the z-score for RM850.<BR>\n" );
document.write( "* Find the area under the standard normal curve to the right of this z-score. This will give you the probability that the sample mean is greater than RM850.\r<BR>\n" );
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document.write( "**d) Exactly RM1000**\r<BR>\n" );
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document.write( "* The probability of the sample mean being exactly equal to the population mean (RM1000) is **zero**. This is because the normal distribution is continuous, and the probability of any single point on a continuous distribution is zero.\r<BR>\n" );
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document.write( "**In summary:**\r<BR>\n" );
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document.write( "* The Central Limit Theorem allows us to approximate the distribution of sample means as normal, even when the population is skewed.<BR>\n" );
document.write( "* We need to know the sample size (n) to calculate the standard error and determine the specific probabilities.<BR>\n" );
document.write( "* The probability of the sample mean being exactly equal to the population mean is always zero for a continuous distribution.\r<BR>\n" );
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document.write( "I hope this explanation helps!<BR>\n" );
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