Question

Decide whether you can use the normal distribution to
approximate the binomial distribution. If you can, use the normal
distribution to approximate the indicated probabilities and sketch
their graphs. If you cannot, explain why and use the binomial
distribution to find the indicated probabilities.

A survey of adults found that 56% of those who text on cell
phones receive spam or unwanted messages. You randomly select 100
adults who text on cell phones.

a-Find the probability that the number of people who receive
spam or unwanted messages is at least 60.

b-Sketch the graph of the normal distribution with the
indicated probability shaded.

Answer #1

This is a binomial distribution question with

n = 100

p = 0.56

q = 1 - p = 0.43999999999999995

This binomial distribution can be approximated as Normal distribution since

np > 5 and nq > 5

Since we know that

a) x = 60

P(x > 60.0)=?

The z-score at x = 60.0 is,

z = 0.8058

This implies that

P(x > 60.0) = P(z > 0.8058) = 1 - 0.7898209109675304

**P(x > 60.0) = 0.2102**

**b)**

Decide whether you can use the normal distribution to
approximate the binomial distribution. If you can, use the normal
distribution to approximate the indicated probabilities and sketch
their graphs. If you cannot, explain why and use the binomial
distribution to find the indicated probabilities. A survey of
adults found that 79% of those who text on cell phones receive
spam or unwanted messages. You randomly select 100 adults who text
on cell phones. Complete parts (a) through (d).
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Decide whether you can use the normal distribution to
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phones receive spam or unwanted messages. You randomly select 100
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Determine whether...

A survey of adults found that 56% of those who text on a cell
phone receive unwanted spam and messages. You randomly pick 100
adults who text on a cell phone. Find the probability that the
number of people who received spam and unwanted messages is exactly
60.

A binomial experiment is given. Decide whether you can use the
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You randomly select 19 parents of teenagers and ask them whether
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np, nq formula
A) Explain when you can use normal distribution to approximate
the binomial distribution
B) If we already know the binomial probability distribution
formula, why do we need to know this one?
C)When is it useful to approximate the binomial distribution as
normal. Provide 1 example

How do you know what functions to use on your calculator when
looking at study problems? For example:
A nationwide study indicated that 80% of college students with
cell phones send and receive
text messages with cell phones. A simple random sample of n = 200
college students with cell phones is
obtained.
(a) Describe the sampling distribution of ˆp, the sample proportion
of college students with cell phones
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Compute P(X) using the binomial probability formula. Then
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By how much do the exact...

Explain how to decide when a normal distribution can be used to
approximate a binomial distribution.
Choose the correct answer below.
A.
If
npgreater than or equals?5
and
nqgreater than or equals??5,
the normal distribution can be used.
B.
If
npnot equals?5
and
nqnot equals??5,
the normal distribution can be used.
C.
If
npless than<5
and
nqless than<?5,
the normal distribution can be used.
D.
If
npgreater than>0
and
nqgreater than>?0,
the normal distribution can be used.

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