Question

a) A Longlife Battery company has developed a battery pack it claims will power a car at a sustained speed of 45 miles per hour for an average of 8 hours. Current data indicate that the standard deviation of battery operation time is 0.4 hours. Data show a Normal distribution of operation time on these battery packs. i) What are the chances of the battery will last 7.5 hours or less when the car is driven at 45 miles per hour? ii) Suppose the automakers will accept no more than 2% chance of the battery lasting 7.5 hours or less, determine the required mean operation time. b) The time taken to deliver the inventory of a manufacturing company is said to be uniformly distributed over the interval of one to four hours. i) State the density function for the delivery time. ii) Calculate the probability that the company will run out of parts due to the shipment taking more than 2 hours. iii) Compute the mean and standard deviation for the delivery time.

          a) A Longlife Battery company has developed a battery pack it claims will power a car at a sustained speed of 45 miles per hour for an average of 8 hours. Current data indicate that the standard deviation of battery operation time is 0.4 hours. Data show a Normal distribution of operation time on these battery packs.

i) What are the chances of the battery will last 7.5 hours or less when the car is driven at 45 miles per hour?

ii) Suppose the automakers will accept no more than 2% chance of the battery lasting 7.5 hours or less, determine the required mean operation time.

b) The time taken to deliver the inventory of a manufacturing company is said to be uniformly distributed over the interval of one to four hours.

i) State the density function for the delivery time.

ii) Calculate the probability that the company will run out of parts due to the shipment taking more than 2 hours.

iii) Compute the mean and standard deviation for the delivery time.

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a) A Longlife Battery company has developed a battery pack it claims will power a car at a sustained speed of 45 miles per hour for an average of 8 hours. Current data indicate that the standard deviation of battery operation time is 0.4 hours. Data show a Normal distribution of operation time on these battery packs.

i) What are the chances of the battery will last 7.5 hours or less when the car is driven at 45 miles per hour?

ii) Suppose the automakers will accept no more than 2% chance of the battery lasting 7.5 hours or less, determine the required mean operation time.

b) The time taken to deliver the inventory of a manufacturing company is said to be uniformly distributed over the interval of one to four hours.

i) State the density function for the delivery time.

ii) Calculate the probability that the company will run out of parts due to the shipment taking more than 2 hours.

iii) Compute the mean and standard deviation for the delivery time.

Added by Kevin T.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Juan Nicolás

01/25/2022

Step 1

4 hours - Operation time follows a normal distribution - We need to find the probability that the battery lasts 7.5 hours or less. Show more…

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Longlife Battery company has developed a battery pack it claims will power a car at a sustained speed of 45 miles per hour for an average of 8 hours. Current data indicate that the standard deviation of battery operational time is 0.4 hours. Data show a normal distribution of operation time on these battery packs. What are the chances of the battery lasting 7.5 hours or less when the car is driven at 45 miles per hour? Suppose the automakers will accept no more than a 2% chance of the battery lasting 7.5 hours or less, determine the required mean operation time. b) The time taken to deliver the inventory of a manufacturing company is said to be uniformly distributed over the interval of one to four hours. State the density function for the delivery time. ii) Calculate the probability that the company will run out of parts due to the shipment taking more than 2 hours. iii) Compute the mean and standard deviation for the delivery time.

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Transcript

00:01 Hello, so today i'm going to answer your question about the performance of a battery and a specific application of the cita test for doing so first i sketch the formula for the ceta test that you need to apply here but x is the value that you want to evaluate me is the mean of the population and is this the standard deviation so the first process that you need to do is replace the value so in this case you want to evaluate that 7 .5 so you need to standardize this value how subtracting by the mean and divided by the standard deviation this gives you 1 .25 the standard value and then you need to evaluate what are the chances that ceta is smaller than 1 minus 1 .25 in this case is 10%.

00:40 So it's quite high in case that for example so in this case you can reject down the hypothesis that is that this value is possible.

00:49 They as well would be the mean to have a value of 2 % so in this case i need to isolate this mu but if you were first finding the value of 2%, that is 2 .05 that would be the ceta value then i take this value and put it in the equation.

01:06 Now i need to isolate this mu.

01:08 What i did here was multiply by 0 .4 or the standard deviation on both sides, and then subtract by 7 .5.

01:15 Then i just simply multiply by minus 1 on both sides, and i know that the mu, the mean need to be 6 .68 to have this percentage with 7 .5.

01:25 Then you need to have an application of the uniform distribution.

01:29 So first, the density function is determined by this formula.

01:31 I just replace 4 and 1 that is the hours that is the remitted.

01:36 This would be the height of the function...

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