Question

Of mountain climbers who attempt Mt. McKinley, only 65% reach the summit. In a random sample of 16 climbers who will make the attempt, what is the probability of each of the following? e.) What is the mean and standard deviation of this study? f.) If 73% of climbers reached the summit, what is the probability that exactly 14 of 16 climbers make it now?

Answer 1

The mean deviation and the stardard deviation are given by the following formulas:

$\sigma=\sqrt[]{\frac{\Sigma(x_i-\mu)^2}{N-1}}$

That formula is for standar deviation in which xi is each value from the population, Miu is the population mean, N is the size of the population.

For the mean deviation, we have the following formula:

$d=\frac{1}{n}\Sigma^n_{i=1}|x_i-m(X)|$

Where m(X) is the average value of the data set, n is the number of data values and xi are the data values in the set.

From this, we will have that the average deviation will be:

$d=\frac{1}{16}\Sigma^{16}_{i=1}|x_i-8.5|\Rightarrow d=0$

And the standar deviation will be:

$\sigma=\sqrt[]{\frac{\Sigma(x_i-8.5)^2}{15}}\Rightarrow\sigma=\frac{2\sqrt[]{51}}{3}\Rightarrow\sigma\approx4.76$

When x = 1 is going to be calculated, when x =2 is going to be calculated and added to the previous value, and so on until It rreaches all the values in the dataset.

Now, if 73% of the climbers reached the summit, the probability that 14 out of 16 will make it now, will be given by:

$p=\frac{n(A)}{n(B)}$

Here n(A) is the number of favorable outcome and n(B) is the total number of favorable outcoles, from this, we have:

$p=\frac{14}{16}\Rightarrow p=0.875$

Why do you say should be 1.91?