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A door delivery florist wishes to estimate the proportion of people in his city that will purchase his flowers. Suppose the true

kvv77 [185]

Answer:

99.74% probability that the sample proportion will be less than 0.1

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using 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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 276, p = 0.06$

So

$\mu = E(X) = np = 276*0.06 = 16.56$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{276*0.06*0.94} = 3.9454$

What is the probability that the sample proportion will be less than 0.1

This is the pvalue of Z when X = 0.1*276 = 27.6. So

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

$Z = \frac{27.6 - 16.56}{3.9454}$

$Z = 2.8$

$Z = 2.8$ has a pvalue of 0.9974

99.74% probability that the sample proportion will be less than 0.1

5 0

4 years ago

Calculate the arithmetic sequence in which a9=17 and the common difference is d=-2.1

jek_recluse [69]

Answer:

$S_{31}=71.3$

Step-by-step explanation:

The nth term of an arithmetic sequence is given by the formula,

$U_n=a_1+(n-1)d$

We were given that the 9th term is $17$ .

$\Rightarrow 17=a_1+(9-1)(-2.1)$

$\Rightarrow 17=a_1+(8)\times(-2.1)$

$\Rightarrow 17=a_1-\frac{84}{5}$

$\Rightarrow 17+\frac{84}{5}=a_1$

$\Rightarrow a_1=\frac{169}{5}$

The sum of the first n-terms is given by the formula,

$S_n=\frac{n}{2}(2a_1+(n-1)d)$

To find $S_{31}$ , we substitute $n=31$ , $a_1=\frac{169}{5}$ and $d=-2.1$ .

$\Rightarrow S_{31}=\frac{31}{2}(2(\frac{169}{5}+(31-1)(-2.1))$

$\Rightarrow S_{31}=\frac{31}{2}(2(\frac{169}{5}+(30)(-2.1))$

$\Rightarrow S_{31}=\frac{31}{2}(\frac{23}{5})$

$\Rightarrow S_{31}=\frac{713}{10}$

$\Rightarrow S_{31}=71.3$

The correct answer is D

8 0

3 years ago

Read 2 more answers

How to find all real solutions

AlladinOne [14]

$\bf \sqrt{\sqrt{x-5}+x}=5\leftarrow \textit{squaring both sides}
\\\\
\sqrt{x-5}+x=25\implies \sqrt{x-5}=25-x\leftarrow \textit{squaring both sides}
\\\\
x-5=(25-x)^2\implies x-5=625-50x+x^2
\\\\
0=x^2-51x+630\implies 0=(x-30)(x-21)$

and surely you'd know what the roots are

7 0

3 years ago

A parachutist's rate during a free fall reaches 180 kilometers per hour. What is this rate in meters per second? At this rate, h

Bumek [7]

Answer:

50 m/s

250 m

Step-by-step explanation:

180 km/hr × (1000 m / km) × (1 hr / 3600 s) = 50 m/s

50 m/s × 5 s = 250 m

5 0

3 years ago