Step 1 From the given information, the mean of women is 63.6 inches and standard deviation is 2.5 inches. Let X be the height of the women follows normal distribution with \(\mu=63.6\ and\ \sigma=2.5.\) Modeling academy standards require women to be models taller than 66 inches Step 2 The percentage of women meet this requirement is, Percentage \(=P(X\ >\ 66)\times 100\%\)
\(=P\left(\frac{X\ -\ \mu}{\sigma}\ >\ (66\ -\ \mu)\sigma\right)\times 100\%\)
\(=P\left(z\ >\ \frac{66\ -\ 63.6}{2.5}\right)\times 100\%\)
\(=P(z\ >\ 0.96)\times 100\%\)
\(=[1\ -\ P(z\ \leq\ 0.96)]\times 100\%\)
\(=0.1685\times 100\%\) from the excel function, \(=1\ −\ NORM.DIST(0.96,\ 0,\ 1,\ TRUE)\)
\(=16.85\%\)
Question
The stature of men is normally distributed, with a mean of 69.0 inches and a standard deviation of 2.8 inches. The height of women is normally distrib
Answers (1)
2021-02-12
Relevant Questions
asked 2021-06-13
1. Who seems to have more variability in their shoe sizes, men or women?
a) Men
b) Women
c) Neither group show variability
d) Flag this Question
2. In general, why use the estimate of \(n-1\) rather than n in the computation of the standard deviation and variance?
a) The estimate n-1 is better because it is used for calculating the population variance and standard deviation
b) The estimate n-1 is never used to calculate the sample variance and standard deviation
c) \(n-1\) provides an unbiased estimate of the population and allows more variability when using a sample and gives a better mathematical estimate of the population
d) The estimate n-1 is better because it is use for calculation of both the population and sample variance as well as standard deviation.
\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 25.7 & M \\ \hline 25.4 & F \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 26.7 & M \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 25.4 & F \\ \hline 25.7 & M \\ \hline 25.7 & F \\ \hline 23.5 & F \\ \hline 23.1 & F \\ \hline 26 & M \\ \hline 23.5 & F \\ \hline 26.7 & F \\ \hline 26 & M \\ \hline 23.1 & F \\ \hline 25.1 & F \\ \hline 27 & M \\ \hline 25.4 & F \\ \hline 23.5 & F \\ \hline 23.8 & F \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline \end{array}\)
\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 27.6 & M \\ \hline 26.9 & F \\ \hline 26 & F \\ \hline 28.4 & M \\ \hline 23.5 & F \\ \hline 27 & F \\ \hline 25.1 & F \\ \hline 28.4 & M \\ \hline 23.1 & F \\ \hline 23.8 & F \\ \hline 26 & F \\ \hline 25.4 & M \\ \hline 23.8 & F \\ \hline 24.8 & M \\ \hline 25.1 & F \\ \hline 24.8 & F \\ \hline 26 & M \\ \hline 25.4 & F \\ \hline 26 & M \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline 27 & M \\ \hline 23.5 & F \\ \hline 29 & F \\ \hline \end{array}\)
a) Men
b) Women
c) Neither group show variability
d) Flag this Question
2. In general, why use the estimate of \(n-1\) rather than n in the computation of the standard deviation and variance?
a) The estimate n-1 is better because it is used for calculating the population variance and standard deviation
b) The estimate n-1 is never used to calculate the sample variance and standard deviation
c) \(n-1\) provides an unbiased estimate of the population and allows more variability when using a sample and gives a better mathematical estimate of the population
d) The estimate n-1 is better because it is use for calculation of both the population and sample variance as well as standard deviation.
\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 25.7 & M \\ \hline 25.4 & F \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 26.7 & M \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 25.4 & F \\ \hline 25.7 & M \\ \hline 25.7 & F \\ \hline 23.5 & F \\ \hline 23.1 & F \\ \hline 26 & M \\ \hline 23.5 & F \\ \hline 26.7 & F \\ \hline 26 & M \\ \hline 23.1 & F \\ \hline 25.1 & F \\ \hline 27 & M \\ \hline 25.4 & F \\ \hline 23.5 & F \\ \hline 23.8 & F \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline \end{array}\)
\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 27.6 & M \\ \hline 26.9 & F \\ \hline 26 & F \\ \hline 28.4 & M \\ \hline 23.5 & F \\ \hline 27 & F \\ \hline 25.1 & F \\ \hline 28.4 & M \\ \hline 23.1 & F \\ \hline 23.8 & F \\ \hline 26 & F \\ \hline 25.4 & M \\ \hline 23.8 & F \\ \hline 24.8 & M \\ \hline 25.1 & F \\ \hline 24.8 & F \\ \hline 26 & M \\ \hline 25.4 & F \\ \hline 26 & M \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline 27 & M \\ \hline 23.5 & F \\ \hline 29 & F \\ \hline \end{array}\)
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If \(X_{1}, X_{2},...,X_{n}\) are Normally distributed with unknown mean 0 and standard deviation 1, then \(\overline{X} \sim N(\frac{0,1}{n})\). Use this result to obtain a pivotal function of X and 0.
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\(\begin{array}{|c|c|} \hline & Housework Hours \\ \hline Gender & Sample\ Size & Mean & Standard\ Deviation \\ \hline Women & 473473 & 33.133.1 & 14.214.2 \\ \hline Men & 488488 & 18.618.6 & 15.715.7 \\ \end{array}\)
a. Based on this study, calculate how many more hours per week, on the average, women spend on housework than men.
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c. Calculate the 95% confidence interval comparing the population means for women Interpret the result including the relevance of 0 being within the interval or not. The 95% confidence interval for \(\displaystyle{\left(\mu_{{W}}-\mu_{{M}}\right)}\) is: (Round to two decimal places as needed.) The values in the 95% confidence interval are less than 0, are greater than 0, include 0, which implies that the population mean for women could be the same as is less than is greater than the population mean for men.
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1. Find each of the requested values for a population with a mean of \(? = 40\), and a
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A. What is the z-score corresponding to \(X = 52?\)
B. What is the X value corresponding to \(z = - 0.50?\)
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