Can anyone help me making sure if my answers is right. Thanks

HELP!!! STATS!!!

Vadim26 [7]

Answer:

The 99% confidence interval is $165.776 < \mu < 180.224$

Step-by-step explanation:

From the question we are told that

The sample size is n = 100

The sample mean is $\= x = 173 \ days$

The population standard deviation is $\sigma = 28 \ days$

From the question we are told the confidence level is 99% , hence the level of significance is

$\alpha = (100 - 99 ) \%$

=> $\alpha = 0.01$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 2.58$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

$E = 2.58 * \frac{28 }{\sqrt{100} }$

=> $E = 7.224$

Generally 95% confidence interval is mathematically represented as

$\= x -E < \mu < \=x +E$

=> $173 -7.224 < \mu < 173 + 7.224$

=> $165.776 < \mu < 180.224$

4 0

2 years ago

In circle O, AD and BE are diameters. What is MAE?

liraira [26]

Answer:

132°

Step-by-step explanation:

∠AOB = ∠EOD = 3x ( vertical angles )

∠AOB + ∠BOC = 90, that is

3x + 0.5x + 34 = 90

3.5x + 34 = 90 ( subtract 34 from both sides )

3.5x = 56 ( divide both sides by 3.5 )

x = 16

∠AOE + ∠EOD = 180 ( straight angle )

∠AOE + 3x = 180

∠AOE + (3 × 16) = 180

∠AOE + 48 = 180 ( subtract 48 from both sides )

∠AOE = 132°

5 0

3 years ago

Read 2 more answers

A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historic

stellarik [79]

Answer:

a) There is a 59.87% probability that none of the LED light bulbs are defective.

b) There is a 31.51% probability that exactly one of the light bulbs is defective.

c) There is a 98.84% probability that two or fewer of the LED light bulbs are defective.

d) There is a 100% probability that three or more of the LED light bulbs are not defective.

Step-by-step explanation:

For each light bulb, there are only two possible outcomes. Either it fails, or it does not. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$n = 10, p = 0.05$

a) None of the LED light bulbs are defective?

This is P(X = 0).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}*(0.05)^{0}*(0.95)^{10} = 0.5987$

There is a 59.87% probability that none of the LED light bulbs are defective.

b) Exactly one of the LED light bulbs is defective?

This is P(X = 1).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{10,1}*(0.05)^{1}*(0.95)^{9} = 0.3151$

There is a 31.51% probability that exactly one of the light bulbs is defective.

c) Two or fewer of the LED light bulbs are defective?

This is

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = 2) = C_{10,2}*(0.05)^{2}*(0.95)^{8} = 0.0746$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.5987 + 0.3151 + 0.0746 0.9884$

There is a 98.84% probability that two or fewer of the LED light bulbs are defective.

d) Three or more of the LED light bulbs are not defective?

Now we use p = 0.95.

Either two or fewer are not defective, or three or more are not defective. The sum of these probabilities is decimal 1.

So

$P(X \leq 2) + P(X \geq 3) = 1$

$P(X \geq 3) = 1 - P(X \leq 2)$

In which

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = 0) = C_{10,0}*(0.95)^{0}*(0.05)^{10}\cong 0$

$P(X = 1) = C_{10,1}*(0.95)^{1}*(0.05)^{9} \cong 0$

$P(X = 2) = C_{10,1}*(0.95)^{2}*(0.05)^{8} \cong 0$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0$

$P(X \geq 3) = 1 - P(X \leq 2) = 1$

There is a 100% probability that three or more of the LED light bulbs are not defective.

8 0

3 years ago

What is the difference between the equations of a vertical and a horizontal line?

svp [43]

Answer:

A horizontal line is a line that is parallel to the x-axis of the coordinate plane and its equation is of the form y = b, where 'b' is constant, whereas, a vertical line is a line parallel to the y-axis and its equation is of the form x = b, where 'b' is constant.

Step-by-step explanation:

4 0

2 years ago

Stephanie was doing a science experiment to see what brand of cereal with raisins

Helen [10]

Answer:

counted 27 raisins. If

there were 12

7 0

3 years ago