Mathematics, 21.04.2020 16:32, eweqwoewoji

On the basis of extensive tests, the yield point of a particular type of mild steel-reinforcing bar is known to be normally distributed with σ = 100. The composition of the bar has been slightly modified, but the modification is not believed to have affected either the normality or the value of σ. 94

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answered: joelhtx

a) $8469-1.645\frac{100}{\sqrt{64}}=8448.4$

$8469+1.645\frac{100}{\sqrt{64}}=8489.6$

So on this case the 90% confidence interval would be given by (8448.4;8489.6)

b) $8469-2.054\frac{100}{\sqrt{64}}=8443.33$

$8469+2.054\frac{100}{\sqrt{64}}=8494.68$

So on this case the 96% confidence interval would be given by (8443.33;8494.68)

Step-by-step explanation:

Assuming this complete problem: On the basis of extensive tests, the yield point of a particular type of mild steel-reinforcing bar is known to be normally distributed with s = 100. The composition of the bar has been slightly modified, but the modification is not believed to have affected either the normality or the value of s.

(a) Assuming this to be the case, if a sample of 64 modified bars resulted in a sample average yield point of 8469 lb, compute a 90% CI for the true average yield point of the modified bar. (Round your answers to one decimal place.)

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=8469$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=100$ represent the population standard deviation

n=64 represent the sample size

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

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

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.645$

Now we have everything in order to replace into formula (1):

$8469-1.645\frac{100}{\sqrt{64}}=8448.4$

$8469+1.645\frac{100}{\sqrt{64}}=8489.6$

So on this case the 90% confidence interval would be given by (8448.4;8489.6)

(b) How would you modify the interval in part (a) to obtain a confidence level of 96%? (Round your answer to two decimal places.)

Since the Confidence is 0.96 or 96%, the value of $\alpha=0.04$ and $\alpha/2 =0.02$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.02,0,1)".And we see that $z_{\alpha/2}=2.054$

Now we have everything in order to replace into formula (1):

$8469-2.054\frac{100}{\sqrt{64}}=8443.33$

$8469+2.054\frac{100}{\sqrt{64}}=8494.68$

So on this case the 96% confidence interval would be given by (8443.33;8494.68)

answered: Guest

saving = more money

step-by-step explanation:

if you have 100 bucks, and you want to buy a candy bar, even if you have one at home, if you choose not to buy it, you save.

~courtney

answered: Guest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.