How would you figure out the answer for this? In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normaldistribution to estimate the requested probabilities.Do you take the free samples offered in supermarkets? About 64% of all customers will take free samples. Furthermore, of those whotake the free samples, about 33% will buy what they have sampled. Suppose you set up a counter in a supermarket offering freesamples of a new product. The day you were offering free samples, 311 customers passed by your counter. (Round your answers tofour decimal places.)(a) What is the probability that more than 180 will take your free sample?(b) What is the probability that fewer than 200 will take your free sample?0.4602(c) What is the probability that a customer will take a free sample and buy the product? Hint: Use the multiplication rule fordependent events. Notice that we are given the conditional probability P(buy|sample) = 0.33, while P(sample) = 0.64.(d) What is the probability that between 60 and 80 customers will take the free sample and buy the product? Hint: Use theprobability of success calculated in part (c).Need Help?Read ItWatch ItMaster It

Name: How would you figure out the answer for this? In the following problem
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: How would you figure out the answer for this? In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normaldistribution to estimate the requested probabilities.Do you take the free samples

n=311p=0.64 np=199.04>10n(1-p)=111.96>10 Since both np and n(1-p) are greater than 10, hence…

Answered: In the following problem, check that it…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

How would you figure out the answer for this?

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal
distribution to estimate the requested probabilities.
Do you take the free samples offered in supermarkets? About 64% of all customers will take free samples. Furthermore, of those who
take the free samples, about 33% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free
samples of a new product. The day you were offering free samples, 311 customers passed by your counter. (Round your answers to
four decimal places.)
(a) What is the probability that more than 180 will take your free sample?
(b) What is the probability that fewer than 200 will take your free sample?
0.4602
(c) What is the probability that a customer will take a free sample and buy the product? Hint: Use the multiplication rule for
dependent events. Notice that we are given the conditional probability P(buy|sample) = 0.33, while P(sample) = 0.64.
(d) What is the probability that between 60 and 80 customers will take the free sample and buy the product? Hint: Use the
probability of success calculated in part (c).
Need Help?
Read It
Watch It
Master It

Expert Solution

Step 1: Introduction and part a)

$n = 311 p = 0.64$

$\begin{array}{rcl} n p & = & 199.04 > 10 \\ n (1 - p) & = & 111.96 > 10 \end{array}$

Since both $n p$ and $n (1 - p)$ are greater than 10, hence normal approximation can be used.

a) Let X be the random variable which denote the number of customer that is take free samples.

$m e a n = μ = n p = 199.04 s \tan d a r d d e v i a t i o n = σ = \sqrt{n p (1 - p)} = 8.4649$

The required probability is

$P (X > 180) = P (\frac{X - μ}{σ} > \frac{180 - 199.04}{8.4649}) = P (Z > - 2.2492) = 0.9878$

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Application of Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions