2. Lindsay, who is the youngest member of the softball team at King's Fork High School, is 7

Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper c

aalyn [17]

Answer:

a) This means that there is a 33% probability that one car chosen at random will have less than 49.5 tons of coal.

b) There is a 0.04% .probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal

Step-by-step explanation:

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.

In this problem, we have that:

The actual weights of coal loaded into each car are normally distributed, with mean = 50 tons and standard deviation = 0.9 ton. This means that $\mu = 50, \sigma = 0.9$

(a) What is the probability that one car chosen at random will have less than 49.5 tons of coal? (Round your answer to four decimal places.)

This is the pvalue of Z when $X = 49.5$

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

$Z = \frac{49.5 - 50}{0.9}$

$Z = -0.44$

$Z = -0.44$ has a pvalue of 0.33.

This means that there is a 33% probability that one car chosen at random will have less than 49.5 tons of coal.

(b) What is the probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal? (Round your answer to four decimal places.)

Now we have to use the standard deviation of the sample, since we are working with the sample mean. That is

$s = \frac{\sigma}{\sqrt{n}} = \frac{0.9}{\sqrt{35}} = 0.15$

Now, we find pvalue of Z when $X = 49.5$

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

$Z = \frac{49.5 - 50}{0.15}$

$Z = -3.33$

$Z = -3.33$ has a pvalue of 0.0004.

This means that there is a 0.04% .probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal

7 0

3 years ago

PLS HELP ASAP I WILL GIVE BRAINERLIST PLUS 10 POINTS

Tresset [83]

It’s the 3rd answer choice

6 0

3 years ago

Explain what can happen if you line up the digits incorrectly when you rewrite addition problems.

melamori03 [73]

You get the answer wrong. E.g. 23.4 + 22.3 = 45.7 BUT if you line it up incorrectly 2.34 + 223. = 225.34

5 0

3 years ago

Read 2 more answers

The mean family income for a random sample of 600 suburban households in Loganville shows that a 95 percent confidence interval

Misha Larkins [42]

Answer:

$43100 \leq \mu \leq 59710$

And for this case we want to test the following hypothesis:

Null hypothesis: $\mu =42000$

Alternative hypothesis: $\mu \neq 42000$

For this case since the lower value of the confidence interval is higher than 42000 we have enough evidence to reject the null hypothesis at the 55 of significance and we can conclude that the true mean is significantly different from 42000

Step-by-step explanation:

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And for this case the 95% confidence interval is already calculated as:

$43100 \leq \mu \leq 59710$

And for this case we want to test the following hypothesis:

Null hypothesis: $\mu =42000$

Alternative hypothesis: $\mu \neq 42000$

For this case since the lower value of the confidence interval is higher than 42000 we have enough evidence to reject the null hypothesis at the 55 of significance and we can conclude that the true mean is significantly different from 42000

7 0

3 years ago

Find the slope and y-intercept of the following graph.

Orlov [11]

Answer: y = -5*x + b

Step-by-step explanation:

A line is written as:

y = a*x + b

where a is the slope and b is the y-intercept.

IIf we have a line that passes through the points (x1, y1) and (x2, y2) then the slope of the line is:

a = (y2 - y1)/(x2 - x1)

In this case we can see that the line passes through the points:

(0, 2) and (1, - 3)

Then the slope is:

a = (-3 - 2)/(1 - 0) = -5

Then our line is:

y = -5*x + b

And when x = 0, y = 2 then:

y = 2 = -5*0 + b

2 = b

Our line is:

y = -5*x + b

6 0

3 years ago