Answered: (a) Find the mean of p, where p is the…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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A minority representation group accuses a major bank of racial discrimination in its recent hires for financial analysts. Exactly 12%of all applications were from minority members, and exactly 10% of the 1650 open positions were filled by members of the minority.

Answer the following.

(a) Find the mean of p, where p is the proportion of minority member applications in a random sample of 1650 that is drawn from all applications.

b) Find the standard deviation of p

c) Compute an approximation for P(p≤1), which is the probability that there will be 10%or fewer minority member applications in a random sample of 1650 drawn from all applications. Round your answer to four decimal places.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

(a)

The mean of p is,

$\begin{array}{rcl} μ & = & p \\ = & 0.12 \end{array}$

Thus, the mean of p is 0.12.

The mean number of minority member applications is $198 (= 0.12 \times 1650)$ .

The standard deviation of p is,

$\begin{array}{rcl} σ & = & \sqrt{\frac{p (1 - p)}{n}} \\ = & \sqrt{\frac{0.12 \times (1 - 0.12)}{1650}} \\ = & \sqrt{0.000064} \\ = & 0.008 \end{array}$

Thus, the standard deviation of p is 0.008.

The number of applications is $13.2 (= 0.008 \times 1650)$ .

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