1) Megan and her husband are two very fertile young newlyweds. Thus, if they have unprotected sexual intercourse, Megan will have a 50% chance of getting pregnant. Soon after said copulation occurs, Megan decides to take a pregnancy test. Despite the claim of being error proof, the box indicates that during the early stages of pregnancy, the probability of seeing a negative result given she is not pregnant is only 93% while the probability of seeing a negative result given she is pregnant is 8%. Megan's pregnancy test displayed a negative result. What is the probability that she is actually pregnant given this negative result (to 4 decimal places)? Use what you know about the Binomial distribution to analyze the following scenarios. For each problem: a) Identify the correct value of all defining parameters. b) Calculate the mean and variance of the distribution. c) Find the indicated probability to 4 decimal places. 2) Assume that each person entering the Apple store has a 30% chance of making a purchase independent of the others. Suppose that 10 potential customers enter the store. Find the probability that fewer than 4 of them make purchases. 3) Seven people are randomly interviewed from a large population that is 55% female. Find the probability that exactly 3 of the selected people are women. 4) A salesman notes that his success rate is about 15%. If he has 20 customers who buy from him independently of the others, find the probability that he makes more than 5 sales. 5) Find the probability that an investor makes a profit on 7 of her next 13 investments, assuming independence and a 0.6 chance of making a profit each time.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1) Megan and her husband are two very fertile young newlyweds. Thus, if they have unprotected sexual intercourse, Megan will have a 50% chance of getting pregnant. Soon after said copulation occurs, Megan decides to take a pregnancy test. Despite the claim of being error proof, the box indicates that during the early stages of pregnancy, the probability of seeing a negative result given she is not pregnant is only 93% while the probability of seeing a negative result given she is pregnant is 8%. Megan's pregnancy test displayed a negative result. What is the probability that she is actually pregnant given this negative result (to 4 decimal places)? Use what you know about the Binomial distribution to analyze the following scenarios. For each problem: a) Identify the correct value of all defining parameters. b) Calculate the mean and variance of the distribution. c) Find the indicated probability to 4 decimal places. 2) Assume that each person entering the Apple store has a 30% chance of making a purchase independent of the others. Suppose that 10 potential customers enter the store. Find the probability that fewer than 4 of them make purchases. 3) Seven people are randomly interviewed from a large population that is 55% female. Find the probability that exactly 3 of the selected people are women. 4) A salesman notes that his success rate is about 15%. If he has 20 customers who buy from him independently of the others, find the probability that he makes more than 5 sales. 5) Find the probability that an investor makes a profit on 7 of her next 13 investments, assuming independence and a 0.6 chance of making a profit each time.

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 + ...

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