Question

You will be performing an analysis on female heights, given of set of 30 heights that were randomly obtained. For this project, it is necessary to know that the average height for women is assumed to be 65 inches with a standard deviation of 3.5 inches. You will use these numbers in some of your calculations.

1. As you know, a random sample of 30 women’s heights was obtained. Describe the sampling distribution. Use a full sentence here to describe the sampling distribution.

2. In StatCrunch or Excel, find and state the mean of the 30 women’s heights that were provided (round to two decimal places). Then (using the values from step 3), calculate the probability that a random sample of 30 women’s heights would result in a mean that was the value you found or more. Use this probability in a full sentence.

72.44   Emma
67.53   Olivia
66.71   Ava
62.02   Isabella
73.89   Sophia
65.95   Mia
65.83   Charlotte
64.15   Amelia
65.39   Evelyn
59.68   Abigail
64.24   Harper
66.6   Emily
65.4   Elizabeth
64.72   Avery
67.11   Sofia
61.97   Ella
62.83   Madison
67.2   Scarlett
66.62   Victoria
68.78   Aria
66.13   Grace
64.47   Chloe
66.64   Camila
62.39   Penelope
63.9   Riley
62.97   Layla
59.31   Lillian
66.14   Nora
67.54   Zoey
63.45   Mila

Answer 1

A sampling distribution is a probability distribution of a statistic obtained from a larger number of samples drawn from a specific population.If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is μ (mu) and the population standard deviation is σ (sigma) then the mean of all sample means (x-bars) is population mean μ (mu).

mean =    ΣX/n =    1962/30=   65.40

µ =    65                  
σ =    3.5                  
                      
P ( X ≥   65.4   ) = P( (X-µ)/σ ≥ (65.4-65) / 3.5)              
= P(Z ≥   0.11   ) = P( Z <   -0.114   ) =    0.4545   (answer)

Please let me know in case of any doubt.

Thanks in advance!

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