6.5.q1 - Student: Grady Si1nonton Colu'se: 1\-Iat11119:...

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Unformatted text preview: Student: Grady Si1nonton Colu'se: 1\-Iat11119: Elementary Statistics - Spring 3010 - C‘RN: 49339 Instructor: Shawn Pan-'ini - 16 weeks Date: 3.-"'18.-"'10 Book: T1‘iola: Elementary Statistics. 11c Time: 4:13 PM Assume that women's heights are normally distributed with a mean given by u = 61.4 in, and a standard deviation given by 0 = 3.7 in. a. If 1 woman is randomly selected, find the probability that her height is less than 62 in. b. If 50 women are randomly selected, find the probability that they have a mean height less than 62 in. a. Notice that an individual value from a normally distributed population has been chosen. Therefore, use the population distribution to determine the probability. x-u First, convert the height to the corresponding 2 score using 2 = and the population distribution statistics. 62—614 3.? as 0.16 z: The probability is the area to the left of z = 0.16 under the standard normal distribution. Look up the area in a table. The area is approximately 0.5636. §=63 it—= 61.4 X Therefore, the probability that a randomly selected woman's height is less than 62 in is approximately 0.5636. b. In this case, the desired probability is for the mean ofa sample of 50 women. Therefore, use the central limit theorem. According to the central limit theorem, the distribution of sample means ; will have a mean given by u; = u and a 0 standard deviation given by 0- = —. x U n The mean of the distribution of sample means ; is the same as the population mean, so u; = 61.4. Apply the definition for the standard deviation of the distribution of the sample means for a sample size of 50. 0' x if? V5 Simplify to find the standard deviation of the distribution of the sample means. Page 1 Student: Grady Sinlonton Course: 1\-Iat11119: Elenlentaiy Statistics - Spring 2010 - C‘RN: 49239 Instructor: Shawn Pan-'ini - 16 weeks Date: 3.-"'18.-"'10 Book: T1‘iola: Elenlentaiy Statistics. Me Time: 4:13 PM 3.7 6-:— x V50 as 0.523259 Therefore, the distribution of sample means ; for a sample size of 50 is approximately normal with a mean u; = 61.4 and a standard deviation 0; = 0.523259. Use these values to compute the corresponding 2 score for ;= 62. 62—614 0.523259 as 1.15 2% The probability is the area to the left of z = 1.15 under the standard normal distribution. Look up the area in a table. The probability is approximately 0.8249. §=63 p—= 61.4 X Therefore, the probability that the mean height of a sample of 50 randomly selected women is less than 62 inches is approximately 0.8249. Page 2 ...
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This note was uploaded on 05/21/2010 for the course MATH 49239 taught by Professor Parvini during the Spring '10 term at Mesa CC.

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6.5.q1 - Student: Grady Si1nonton Colu'se: 1\-Iat11119:...

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