Questions: have mean length of 12 cm with a standard deviation of 0.05 cm. For what lengths will a bot be destroyed? Select the correct choice below and fill in the answer box(s) to complete your choice (Round to one decimal place as needed) A. A bot will be destroyed if the length is between cm and km B. A bot will be destroyed if the length is less than cm C. A bot will be destroyed if the length is less than cm or greater than cm. D. A bolt will be destroyed if the length is greater than cm.

have mean length of 12 cm with a standard deviation of 0.05 cm. For what lengths will a bot be destroyed? Select the correct choice below and fill in the answer box(s) to complete your choice (Round to one decimal place as needed) A. A bot will be destroyed if the length is between cm and km B. A bot will be destroyed if the length is less than cm C. A bot will be destroyed if the length is less than cm or greater than cm. D. A bolt will be destroyed if the length is greater than cm.
Transcript text: have mean lengh of 12 cm whin a standard deviation of 005 cm . For what lengts will a bot be destroyed? Select the correct choice below and fill in the answer box(s) to complete your choice (Round to one decimal place as needed) A. A bot will be destroyed if the length is between $\square$ cm and $\square$ km B. A bot will be destroyed if the lengh is less than $\square$ cm C. A bot will be destrojed if the length is less than $\square$ om or greater than $\square$ cm. D. A bolt will be destroyed it the longth is greater than $\square \mathrm{cm}$.
failed

Solution

failed
failed

Solution Steps

Step 1: Given Information

We are provided with the following parameters for the lengths of bolts:

  • Mean length (\( \mu \)) = 12 cm
  • Standard deviation (\( \sigma \)) = 0.05 cm
Step 2: Determine Destruction Criteria

To determine the lengths at which a bolt will be destroyed, we apply the 3-sigma rule. A bolt is considered destroyed if its length is more than 3 standard deviations away from the mean. This can be expressed mathematically as:

\[ \text{Destruction Criteria: } L < \mu - 3\sigma \quad \text{or} \quad L > \mu + 3\sigma \]

Step 3: Calculate the Bounds

We calculate the lower and upper bounds using the mean and standard deviation:

\[ \text{Lower Bound} = \mu - 3\sigma = 12 - 3 \times 0.05 = 12 - 0.15 = 11.85 \text{ cm} \]

\[ \text{Upper Bound} = \mu + 3\sigma = 12 + 3 \times 0.05 = 12 + 0.15 = 12.15 \text{ cm} \]

Step 4: State the Final Destruction Lengths

Thus, a bolt will be destroyed if its length is less than \( 11.85 \) cm or greater than \( 12.15 \) cm.

Final Answer

A bolt will be destroyed if the length is less than \( 11.8 \) cm or greater than \( 12.2 \) cm.

The answer is C.

\[ \boxed{L < 11.8 \text{ cm} \text{ or } L > 12.2 \text{ cm}} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
The first three terms of an arithmetic sequence are as follows. -19, -14, -9 Find the next two terms of this sequence. -19, -14, -9,
failedAnswered
What is the population of interest?
failedAnswered
Find all solutions to the equation (4 tan ^3(x)-4 tan (x)=0) over the interval (0, pi)). A) (x=0, x=fracpi4) B) (x=0, x=fracpi4, x=frac3 pi4) C) (x=0, x=fracpi4, x=frac5 pi4) D) (x=0, x=fracpi4, x=frac-pi4) E) (x=0, x=fracpi4, x=fracpi2) F) None of the above
failedAnswered
Graph the function and its parent function. Then describe the transformation. g(x) = 1/2(x+2)^2 + 3 a. The graph of g is a translation 2 units right, a vertical shrink, and a translation 3 units down of the parent quadratic function. b. The graph of g is a translation 2 units right, a vertical shrink, and a translation 3 units up of the parent quadratic function. c. The graph of g is a translation 2 units
failedAnswered
How long will it take (a) a 1000 W heater to evaporate 1.0 kg of water that is already at 100°C, its normal boiling point (b) a refrigerator to freeze 0.40 kg of water that is already at 0°C, its normal freezing point, if it can remove energy at an average rate of 75 W?