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Aleonysh [2.5K]

3 years ago

5

Alice has seven times the amount of pens that Maurice has. Paul has two-thirds of the amount of pens as Alice and Suzy have comb

ined. Dawn has a dozen more pens than Paul. Suzy has half the pens that Maurice has. If Suzy has 2 pens, how many does Dawn have?

1 answer:

zepelin [54]3 years ago

5 0

Answer:

Dawn has 32 pens.

Step-by-step explanation:

Let No. of pens Alice has = A
Let No. of pens Maurice has = M
Let no of pens Paul has = P
Let no. of pens Suzy has = S
Let no of pens Dawn has = D

Given :

A = 7M
P = 2/3 (A + S)
D = P + 12
S = 1/2 M

If S = 2 {Given}
M = 4 [∵ S = 1/2 M → M = 2S = 2X(2) ]
A = 28 [ ∵ A = 7M → A = 7 x 4 ]
P = 20 [∵ P = 2/3 (A+S) → P = 2/3 (28 + 2) = 2/3 (30) ]
D = 32 [ ∵ D = P + 12 → D = 20 + 12 ]

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Answer:

a) 37.31 b) 42.70 c) 0.57 d) 0.09

Step-by-step explaanation:

We are regarding a normal distribution with a mean of 35 and a standard deviation of 6, i.e., $\mu$ = 35 and $\sigma$ = 6. We know that the probability density function for a normal distribution with a mean of $\mu$ and a standard deviation of $\sigma$ is given by

$f(x) = \frac{1}{\sqrt{2\pi}\sigma}\exp[-\frac{(x-\mu)^{2}}{2\sigma^{2}}]$

in this case we have

$f(x) = \frac{1}{\sqrt{2\pi}6}\exp[-\frac{(x-35)^{2}}{2(6^{2})}]$

Let $X$ be the random variable that represents a row score, we find the values we are seeking in the following way

a) we are looking for a number $x_{0}$ such that

$P(X\leq x_{0})$ = $\int\limits^{x_{0}}_{-\infty} {f(x)} \, dx = 0.65$ , this number is $x_{0}$ =37.31

you can find this answer using the R statistical programming languange and the instruction qnorm(0.65, mean = 35, sd = 6)

b) we are looking for a number $x_{1}$ such that

$P(X\leq x_{1})$ = $\int\limits^{x_{1}}_{-\infty} {f(x)} \, dx = 0.9$ , this number is $x_{1}$ =42.70

you can find this answer using the R statistical programming languange and the instruction qnorm(0.9, mean = 35, sd = 6)

c) we find this probability as

$P(28\leq X\leq 38)$ = $\int\limits^{38}_{28} {f(x)} \, dx = 0.57$

you can find this answer using the R statistical programming languange and the instruction pnorm(38, mean = 35, sd = 6) -pnorm(28, mean = 35, sd = 6)

d) we find this probability as

$P(41\leq X\leq 44)$ = $\int\limits^{44}_{41} {f(x)} \, dx = 0.09$

you can find this answer using the R statistical programming languange and the instruction pnorm(44, mean = 35, sd = 6) -pnorm(41, mean = 35, sd = 6)

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3 years ago

Read 2 more answers

A sample with a mean of m = 40 and a variance of s2 = 20 has an estimated standard error of 1 point. how many scores are in the

tamaranim1 [39]

The correct option is 20.

The score found for the sample is 20.

<h3>What is Standard error?</h3>

A standard error is a statistic that is applied to test the distribution of data. This metric is comparable to standard deviation. We can calculate the standard error if we know the sample size & standard deviation. It assesses the mean's precision.

Now, according to the question;

Sample mean; $\bar{x}=40$

Sample variance; $s^{2}=20$

Thus, $s=\sqrt{20}=4.47$

Standard error SE = 1

The amount of scores with in sample must be determined here.

The standard error formula is as follows:

$S E=\frac{s}{\sqrt{n}}$

We might rearrange the formula as follows:

$\begin{aligned}\sqrt{n} &=\frac{s}{S E} \\n &=\left(\frac{s}{S E}\right)^{2}\end{aligned}$

Substituting the values;

$\begin{aligned}&n=\left(\frac{4.47}{1}\right)^{2} \\&n=19.98\end{aligned}$

The sample's number of scores n = 19.98 = 20 (round up)

Therefore, the scores are in the sample is 20.

To know more about the Standard error, here

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