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3 years ago

Please help with this normal distribution problem

Mathematics

2 answers:

konstantin123 [22]3 years ago

8 0

900 = 750 + 2*75. In other words, 900 is 2 standard deviations away from the mean. Similarly, 975 is 3 standard deviations from the mean. So

$P(900$ is the random variable for the lifespan of a light bulb with the given normal distribution, and $Z=\dfrac{X-750}{75}$ with the standard normal distribution.

We get

$P(2$

If you don't have a calculator/lookup table available, you can invoke the empirical rule, the one that says

$\begin{cases}P(-1$

The normal distribution is symmetric about its mean, so we also know

$\begin{cases}P(0$

Then

$P(2$

liberstina [14]3 years ago

7 0

Answer:

0.021

Step-by-step explanation:

One way in which to approach this problem solution is to use a calculator that has statistical distribution functions built in. My old TI-83Plus has the function "normalcdf," which does the job nicely.

Typing in normalcdf(900,975,750,75) results in the probability 0.021 that a light bulb chosen at random will last between 900 and 975 hours.

Using a table of z-scores would be a good alternative approach. Note that the z-score corresponding to 750 hours is 0; that for 900 is +2; and that for 975 is +3. Find the area under the standard normal curve to the left of 975 (z = 3) and that to the left of 900 (z = 2), and then subtract the two results. It will be 0.021, as before.

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A researcher compares the effectiveness of two different instructional methods for teaching physiology. A sample of 178 students

xxTIMURxx [149]

Answer:

critical value = 1.645

The 90% confidence interval = ( -22.62, -17.58)

Step-by-step explanation:

Given that:

the sample size $n_1$ = 178

the sample size $n_2$ = 226

the sample mean $\overline x_1$ = 54.4

the sample mean $\overline x_2$ = 74.5

population standard deviation $\sigma_1$ = 18.58

population standard deviation $\sigma_2$ = 9.52

level of significance ∝ = 1 - 0.90 = 0.10

The critical value for $Z_{\alpha/2} = Z _{0.10/2} = Z_{0.005}$ is 1.645

For the construction of our confidence interval, we use 90% since that is used to find the critical value.

∴

The margin of error = $Z \times\sqrt{\dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma_2^2}{n_2}}$

$1.645 \times\sqrt{\dfrac{18.58^2}{178} + \dfrac{9.52^2}{226}}$

$1.645 \times\sqrt{\dfrac{345.2164}{178} + \dfrac{90.6304}{226}}$

$1.645 \times\sqrt{2.34042}$

$\simeq$ 2.52

The lower limit = $( \overline x_1 - \overline x_2) - (M.O.E)$

= ( 54.4-74.5) - (2.52)

= -20.1 - 2.52

= -22.62

The upper limit = $( \overline x_1 - \overline x_2) + (M.O.E)$

= ( 54.4-74.5) + (2.52)

= -20.1 + 2.52

= -17.58

The 90% confidence interval = ( -22.62, -17.58)

6 0

3 years ago

Help me on this problem

rjkz [21]

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4 years ago

What is the Standard Form of the line with x-intercept of 6 and y-intercept of 5?

kolbaska11 [484]

keeping in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$\bf \stackrel{\textit{x-intercept}}{(\stackrel{x_1}{6}~,~\stackrel{y_1}{0})}\qquad \stackrel{\textit{y-intercept}}{(\stackrel{x_2}{0}~,~\stackrel{y_2}{5})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{6}}}\implies -\cfrac{5}{6}$

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3 years ago

Which is correct?

Alja [10]

Below is the conversion table for letter A to D:
1 deciliter = 0.001 hectoliters
1 liter = 100 centiliters
1 kilolieter = 10 hectoliter
1 liter = 10 deciliter

The correct one would be letter C - There are 6.8 kiloliters in 68 hectoliters. Since 1 kiloliters (kl) is equal to 10 hectoliters (hl), 6.8 kl times 10 is equal to 68 hl.

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4 years ago

A gas station customer pumps exactly six gallons

ki77a [65]

Answer:

Please find attached the graph of the relationship between the gallons, g, and cost, C

The relationship between the cost and number of gallons is cost C = $3.25 × Number of gallons, g

Step-by-step explanation:

The given parameters are;

Number of Gallons, g ${}$ Cost, C

6 ${}$ $19.50 ${}$

22 $71.50

From the given coordinates, we generate the graph using Microsoft Excel, as seen in the attached graph

The given coordinates can be used to find the equation of the relationship in point and slope form as follows;

The slope of the the given coordinates are (71.5 - 19.5)/(22 - 6) = 3.25

The equation of the graph in point and slope form is C - 71.5 = 3.25·(g - 22)

C - 71.5 = 3.25·(g - 22)

C = 3.25·g - 3.25 × 22 + 71.5 = 3.25·g - 0

C = 3.25·g

The relationship between the cost and number of gallons is cost C = $3.25 × Number of gallons, g

From the above equation, we have, that the price per gallon is $3.25

7 0

3 years ago