When solving a mass/particle or particle/mass conversion calculation what piece(s)

Suppose that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to

polet [3.4K]

Answer:

(a) The probability that X is at most 30 is 0.9726.

(b) The probability that X is less than 30 is 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is 0.7406.

Step-by-step explanation:

We are given that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked. A random sample of 200 shafts is taken.

Let X = the number among these that are nonconforming and can be reworked

The above situation can be represented through binomial distribution such that X ~ Binom(n = 200, p = 0.11).

Here the probability of success is 11% that this much % of all steel shafts produced by a certain process are nonconforming but can be reworked.

Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).

So, the new mean of X, $\mu$ = $n \times p$ = $200 \times 0.11$ = 22

and the new standard deviation of X, $\sigma$ = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{200 \times 0.11 \times (1-0.11)}$

= 4.42

So, X ~ Normal( $\mu =22, \sigma^{2} = 4.42^{2}$ )

(a) The probability that X is at most 30 is given by = P(X < 30.5) {using continuity correction}

P(X < 30.5) = P( $\frac{X-\mu}{\sigma}$ < $\frac{30.5-22}{4.42}$ ) = P(Z < 1.92) = 0.9726

The above probability is calculated by looking at the value of x = 1.92 in the z table which has an area of 0.9726.

(b) The probability that X is less than 30 is given by = P(X $\leq$ 29.5) {using continuity correction}

P(X $\leq$ 29.5) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{29.5-22}{4.42}$ ) = P(Z $\leq$ 1.70) = 0.9554

The above probability is calculated by looking at the value of x = 1.70 in the z table which has an area of 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is given by = P(15 $\leq$ X $\leq$ 25) = P(X < 25.5) - P(X $\leq$ 14.5) {using continuity correction}

P(X < 25.5) = P( $\frac{X-\mu}{\sigma}$ < $\frac{25.5-22}{4.42}$ ) = P(Z < 0.79) = 0.7852

P(X $\leq$ 14.5) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{14.5-22}{4.42}$ ) = P(Z $\leq$ -1.70) = 1 - P(Z < 1.70)

= 1 - 0.9554 = 0.0446

The above probability is calculated by looking at the value of x = 0.79 and x = 1.70 in the z table which has an area of 0.7852 and 0.9554.

Therefore, P(15 $\leq$ X $\leq$ 25) = 0.7852 - 0.0446 = 0.7406.

5 0

3 years ago

Pine Street intersects Center Street at a 65 degree angle. If center Street is parallel to First Avenue, which equation is true?

Nimfa-mama [501]

The answer would be x=180-65 this is because vertically opposite angle to 65 would be 65 which means that x and 65 are supplementary.

5 0

4 years ago

Read 2 more answers

lenny deposits $7,000 in an IRA. What will be the value of his investment in 3 years if the investment is earning 1.95% per year

lorasvet [3.4K]

Step-by-step explanation:

The interest is 1.95 percent.

1.95 percent = 1.0195

Value after 3 years =

$1.0195 {}^{3} \times 7000$

= $7417.54 (to the nearest cent)

4 0

3 years ago

Read 2 more answers

Do I have to solve this before graphing it and if so how do I go about it?

defon

Given the System of Equations:

$\begin{cases}y=4x-1 \\ \\ y=x-4\end{cases}$

The exercise asks for solving it graphically. Then, in this case, you need to graph both lines in order to determine the solution of the system.

In order to graph it, you can find the x-intercepts and the y-intercepts:

1. It is important to remember the Slope-Intercept Form of the equation of a line:

$y=mx+b$

Where "m" is the slope of the line and "b" is the intercept.

In this case, you can identify that the y-intercept of the first line is:

$b_1=-1$

And the y-intercept of the second line is:

$b=-4$

2. By definition, the value of "y" is zero when the line intersects the x-axis.

Then, you need to substitute the following value of "y" into each equation and then solve for "x", in order to find the x-intercept of each line:

$y=0$

- For the first line, you get:

$\begin{gathered} y=4x-1 \\ 0=4x-1 \\ 1=4x \\ \\ \frac{1}{4}=x \\ \\ x_1=0.25 \end{gathered}$

- For the second line, you get:

$\begin{gathered} y=x-4 \\ 0=x-4 \\ 4=x \\ x_2=4 \end{gathered}$

3. Now you know that the first line passes through these two points:

$(0.25,0);(0,-1)$

And the second line passes through these two points:

$(4,0);(0,-4)$

4. Knowing those points, you can graph the lines:

Notice that the line intersect each other at

5 0

1 year ago

Jenny made $221 for 13 hours of work. At the same rate, how many hours would she have to work to make $85?

Sever21 [200]

Answer: Jenny would have to work 5 hours to get $85

Step-by-step explanation:

Jenny makes $17 an hour (221/13 = 17) and 85/17 is 5

5 0

3 years ago