Does the exponential function, y=(0.15)^x, model exponential growth, or exponential decay?

A telephone exchange operator assumes that 8% of the phone calls are wrong numbers. If the operator is right, what is the probab

Vera_Pavlovna [14]

Answer:

The probability that the sample proportion differ from the population proportion by greater than 3% is 0.0241.

Step-by-step explanation:

Let X = number of phone calls that are wrong numbers.

The proportion of phone calls that are wrong numbers is, p = 0.08.

A sample of n = 421 phone calls is selected to determine the proportion of wrong numbers in this sample.

The random variable X follows a Binomial distribution with parameters n and p.

The probability mass function of a Binomial distribution is:

$P(X=x)={421\choose x}0.08^{x}(1-0.08)^{421-x}$

Now, for the sample proportion to differ from the population proportion by 3% the value of the sample proportion should be:

$\hat p-p=0.03\\\hat p-0.08=0.03\\\hat p=0.11$ $\hat p-p=-0.03\\\hat p-0.08=-0.03\\\hat p=0.05$

So when the sample proportion is less than 5% or greater than 11% the difference between the sample proportion and population proportion will be greater than 3%.

If sample proportion is 5% then the value of X is,

$X=np=421\times 0.05=21.05\approx21$

Compute the value of P (X ≤ 21) as follows:

$P(X\leq 21)=\sum\limits^{21}_{x=0}{{421\choose x}0.08^{x}(1-0.08)^{421-x}}=0.0106$

If the sample proportion is 11% then the value of X is,

$X=np=421\times 0.11=46.31\approx47$

Compute the value of P (X ≥ 47) as follows:

$P(X\geq 47)=\sum\limits^{471}_{x=47}{{421\choose x}0.08^{x}(1-0.08)^{421-x}}=0.0135$

Then the probability that the sample proportion differ from the population proportion by greater than 3% is:

$P(\hat p-p>0.03)=P(X\leq 21)+P(X\geq 47)=0.0106+0.0135=0.0241$

Thus, the probability that the sample proportion differ from the population proportion by greater than 3% is 0.0241.

7 0

3 years ago

Simplify −6+13x−7−16x.

mars1129 [50]

Answer: -13-3X
Combine like terms.
-6-7= -13
13X- 16X= -3X

7 0

3 years ago

Read 2 more answers

Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.

Gnom [1K]

Answer:x

Step-by-step explanation:

4 0

3 years ago

A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimat

zmey [24]

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .