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ratelena [41]
3 years ago
11

your mum has saved £12000 and agreed to give you a share, would you rather have 1 fith or 1 tenth of a share

Mathematics
2 answers:
nydimaria [60]3 years ago
7 0

obv. everyone would want to have 1 fifth


Rufina [12.5K]3 years ago
3 0
1 fifth of the share is a much better choice that 1 tenth of the share.
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The temperature of a certain solution is estimated by taking a large number of independent measurements and averaging them. The
Mademuasel [1]

Answer:

(a) The 95% confidence interval for the temperature is (36.80°C, 37.20°C).

(b) The confidence level is 68%.

(c) The necessary assumption is that the population is normally distributed.

(d) The 95% confidence interval for the temperature if 10 measurements were made is (36.93°C, 37.07°C).

Step-by-step explanation:

Let <em>X</em> = temperature of a certain solution.

The estimated mean temperature is, \bar x=37^{o}C.

The estimated standard deviation is, s=0.1^{o}C.

(a)

The general form of a (1 - <em>α</em>)% confidence interval is:

CI=SS\pm CV\times SD

Here,

SS = sample statistic

CV = critical value

SD = standard deviation

It is provided that a large number of independent measurements are taken to estimate the mean and standard deviation.

Since the sample size is large use a <em>z</em>-confidence interval.

The critical value of <em>z</em> for 95% confidence interval is:

z_{0.025}=1.96

Compute the confidence interval as follows:

CI=SS\pm CV\times SD\\=37\pm 1.96\times 0.1\\=37\pm0.196\\=(36.804, 37.196)\\\approx (36.80^{o}C, 37.20^{o}C)

Thus, the 95% confidence interval for the temperature is (36.80°C, 37.20°C).

(b)

The confidence interval is, 37 ± 0.1°C.

Comparing the confidence interval with the general form:

37\pm 0.1=SS\pm CV\times SD

The critical value is,

CV = 1

Compute the value of P (-1 < Z < 1) as follows:

P(-1

The percentage of <em>z</em>-distribution between -1 and 1 is, 68%.

Thus, the confidence level is 68%.

(c)

The confidence interval for population mean can be constructed using either the <em>z</em>-interval or <em>t</em>-interval.

If the sample selected is small and the standard deviation is estimated from the sample, then a <em>t</em>-interval will be used to construct the confidence interval.

But this will be possible only if we assume that the population from which the sample is selected is Normally distributed.

Thus, the necessary assumption is that the population is normally distributed.

(d)

For <em>n</em> = 10 compute a 95% confidence interval for the temperature as follows:

The (1 - <em>α</em>)% <em>t</em>-confidence interval is:

CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}

The critical value of <em>t</em> is:

t_{\alpha/2, (n-1)}=t_{0.025, 9}=2.262

*Use a <em>t</em>-table for the critical value.

The 95% confidence interval is:

CI=37\pm 2.262\times \frac{0.1}{\sqrt{10}}\\=37\pm 0.072\\=(36.928, 37.072)\\\approx (36.93^{o}C, 37.07^{o}C)

Thus, the 95% confidence interval for the temperature if 10 measurements were made is (36.93°C, 37.07°C).

3 0
3 years ago
The record high temperature in January was 18 degrees. The record low temperature was –7 degrees. What is the amount of change b
vodka [1.7K]

Answer: 25^{\circ}

Step-by-step explanation:

Given

The highest temperature recorded is 18^{\circ}

The lowest temperature recorded is -7^{\circ}

The amount of change between the high and the low temperatures is

\Rightarrow 18-(-7)=18+7\\\Rightarrow 25^{\circ}

6 0
3 years ago
What does 6×3+(9-3)+1 equal?
Lelu [443]
Hi

6*3 + (9-3)
= 18 + 3
= 21

I hope that's help !
3 0
3 years ago
Read 2 more answers
(9Q) Solve the log.
Arada [10]

Answer:

D

Step-by-step explanation:

3 0
3 years ago
tom keeps all of his favorite marbles in a special leather bag. right now, fove red marbles, four blue marbles, and three yellow
arlik [135]
4/12 simplified will be 1/3
Answer is 1/3.
4 0
3 years ago
Read 2 more answers
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