The height of adult women in North America are normally distributed with a mean
ID: 2953725 • Letter: T
Question
The height of adult women in North America are normally distributed with a mean of 65in. and a standard deviation of 3.5in. To be a Rockette a women has to be between 5'6'' and 5'10'' tall 1) Find the probability that a randomly sellected sample of 25 women have a mean height between 5'6'' and 5'10'' tall. i) What is the shape of the distribution? How do you know this? ii) Draw the distribution, lablel the x value and/or z value, shade the area we are concerned with iii) Calculate the probability and then state your answer in a summary sentense 2) Which is more likely, selecting a single women with a height in this range or a group of 25 women with an average height in this range? why ?Explanation / Answer
The height of adult women in North America are normallydistributed with a mean of 65in. and a standard deviation of 3.5in.To be a Rockette a women has to be between 5'6'' and 5'10'' tall 1)Find the probability that a randomly sellected sample of 25 womenhave a mean height between 5'6'' and 5'10'' tall. i) What is theshape of the distribution? How do you know this? ii) Draw thedistribution, lablel the x value and/or z value, shade the area weare concerned with iii) Calculate the probability and then stateyour answer in a summary sentense 2) Which is more likely,selecting a single women with a height in this range or a group of25 women with an average height in this range? why ?First of all I converted the requirements of the height from5'6" and 5'10" to 66" and 70". 1. To find the probability, use this equation: / ( / n) = z 66 / (3.5 / 25) = z 70 / (3.5 / 25) = z Use this with the z table to find the probability from themean. Subtract the answers and that is your answer to the firstpart. 1i. I think the shape of this distribution is negativelyskewed, because the mean is less than the range we are lookingfor. 1ii. Should be easy enough from here! 1iii. See the first part lol! 2. The easiest way to do this part is to repeat the first stepwithout the n size using this equation: / = z 66 / 3.5 = z 70 / 3.5 = z Use this with the z table to find the probability from themean. Subtract the answers and that is your answer to the firstpart. Then compare the answers to understand why it's easier to findone needle in the hay over 25 needles! LOL! The height of adult women in North America are normallydistributed with a mean of 65in. and a standard deviation of 3.5in.To be a Rockette a women has to be between 5'6'' and 5'10'' tall 1)Find the probability that a randomly sellected sample of 25 womenhave a mean height between 5'6'' and 5'10'' tall. i) What is theshape of the distribution? How do you know this? ii) Draw thedistribution, lablel the x value and/or z value, shade the area weare concerned with iii) Calculate the probability and then stateyour answer in a summary sentense 2) Which is more likely,selecting a single women with a height in this range or a group of25 women with an average height in this range? why ?
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