Please help ASAP help please

) To estimate weight of a certain product, 100 of these products are measured. The average weight and standard deviation are cal

inessss [21]

Answer:

a) $P(X$

And we can find this probability with the normal standard table or excel and we got:

$P(z$

And we would expect about 0.02275*10000 =227.5 rejected and 2.75 in the sample of 100 selected

b) $P(39$

And we can find this probability with this difference:

$P(-1$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-1$

And we expect about 0.819*10000= 8190 and 81.9 in the sample od 100 selected

c) $40-1.64\frac{1}{\sqrt{100}}=39.836$

$40+1.64\frac{1}{\sqrt{100}}=40.164$

So on this case the 90% confidence interval would be given by (39.836;40.164)

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(40,1)$

Where $\mu=40$ and $\sigma=1$

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability with the normal standard table or excel and we got:

$P(z$

And we would expect about 0.02275*10000 =227.5 rejected and 2.75 in the sample of 100 selected

Part b

$P(39$

And we can find this probability with this difference:

$P(-1$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-1$

And we expect about 0.819*10000= 8190 and 81.9 in the sample od 100 selected

Part c

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 $z_{\alpha/2}=1.64$