‘Basic exponent rules’ simplifying to a single power .

A machine making computer chips isn't working correctly, and 5% of the computer chips it makes are defective. If an inspector ch

Rainbow [258]

Answer:

0.25% probability that they are both defective

Step-by-step explanation:

For each computer chip, there are only two possible outcomes. Either they are defective, or they are not. The probability of a computer chip being defective is independent of other chips. So we use the binomial probability distribution to solve this question.

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 combinations 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.

5% of the computer chips it makes are defective.

This means that $p = 0.05$

If an inspector chooses two computer chips randomly (meaning they are independent from each other), what is the probability that they are both defective?

This is P(X = 2) when n = 2. So

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

$P(X = 2) = C_{2,2}.(0.05)^{2}.(0.95)^{0} = 0.0025$

0.25% probability that they are both defective

4 0

2 years ago

Can you guys please help me get the right answer I already got one wrong I can’t get another wrong!❤️

katrin2010 [14]

Answer:

C. The area is 900 square feet

Step-by-step explanation:

A square has four equal sides, and if one side is 30 feet then all sides are 30 feet. The formula for a square is A=s2

A=30 squared

A=900 square feet

7 0

3 years ago

Read 2 more answers

Help and get 6 points!

timofeeve [1]

10 hours was the full time she painted

7 0

3 years ago

Read 2 more answers

While conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modem

Kitty [74]

Answer:

We conclude that this is an unusually high number of faulty modems.

Step-by-step explanation:

We are given that while conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems.

The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013.

Let p = population proportion.

So, Null Hypothesis, $H_0$ : p = 0.013 {means that this is an unusually 0.013 proportion of faulty modems}

Alternate Hypothesis, $H_A$ : p > 0.013 {means that this is an unusually high number of faulty modems}

The test statistics that would be used here One-sample z-test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion faulty modems= $\frac{10}{367}$ = 0.027

n = sample of modems = 367

So, the test statistics = $\frac{0.027-0.013}{\sqrt{\frac{0.013(1-0.013)}{367} } }$

= 2.367

The value of z-test statistics is 2.367.

Since, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since our test statistics is more than the critical value of z as 2.367 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that this is an unusually high number of faulty modems.

6 0

3 years ago

Use the function g(x)-x+2 with initial values of 4, 2, and 1. What happens

kolezko [41]

Answer:

Step-by-step explanation:

The given function is , g(x)= - x + 2

For values of , is the sequence, -2,4,-2,4,-2,4........

For values of , is the sequence, 0,2,0,2........

For values of , is the sequence, 1,1,1,1,........

For initial value, of 4,the sequence converges to two values that is -2, 4.

For initial value of 2, the sequence again converges to two values which are 0,2.

For initial value of 1, the sequence converges to one value which is 1.

→→First Iterative value that is (-2)=Second iterative value (0) + 2 ×Third iterative value(1)

→→ First Iterative value that is (4)=Second iterative value (2) + 2 ×Third iterative value(1)

4 0

3 years ago