PLZ help me and anyone who can help me will get 15 points

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

Rebecca is a Texas resident and she plans to attend Texas Tech for all 4 years of college. She has a yearly scholarship of $10,0

andrezito [222]

Answer:

To complete the required $m dollars for her college, she needs $(m - 60,000).

Step-by-step explanation:

Suppose Rebecca needs $m to complete her college education,

because she has a yearly scholarship of $10,000, she would have $10,000 × 4 = $40,000 for the four years she would spend in college.

Together with her savings of $20,000, she has $20,000 + $40,000 = $60,000 in total.

Therefore to complete the required $m dollars for her college, she needs $(m - 60,000).

5 0

2 years ago

If the endpoints of the diameter of a circle are (−10, −8) and (−6, −2), what is the standard form equation of the circle? A) (x

kolbaska11 [484]

Selections B and D both appear to be appropriate.
B) (x+8)² + (y+5)² = 13
D) (x+8)² + (y+5)² = 13

_____
The center is at the midpoint of the diameter, ((-10-6)/2, (-8-2)/2) = (-8, -5). For center (h, k) and radius r, the equation is
(x -h)² +(y -k)² = r²
(x -(-8))² +(y -(-5))² = (√13)²
(x+8)² + (y+5)² = 13

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3 years ago

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bazaltina [42]

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15 15 goes into 45 5 times and 60 5 times. highest number that goes into both numbers evenly

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