# The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However, records indicate that the mean time is 16.2 minutes, and the standard deviation is 3.4 minutes.Requried:a. What is the probabilty that a random sample of n = 40 oil changes results in a sample mean time less than 15 minutes?b. Suppose the manager agrees to pay each employee a​ \$50 bonus if they meet a certain goal. On a typical​ Saturday, the​ oil-change facility will perform 40 oil changes between 10 A.M. and 12 P.M. Treating this as a random​ sample, there would be a​ 10% chance of the mean​ oil-change time being at or below what​ value? This will be the goal established by the manager.

(a) Probability that a random sample of n = 45 oil changes results in a sample mean time < 10 ​minutes i=0.0001.

(b) The mean oil-change time is 15.55 minutes.

Step-by-step explanation:

Let us denote the sample mean time as x

From the Then x = mean time = 16.2 minutes

The given standard deviation = 3.4 minutes

The value of  n sample size = 45

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

## Related Questions

2. Half of the pieces of fruit in the bowl are apples. There arealso 3 oranges, 2 pears, and a banana.
How many apples are there in the bowl? Show your work!

6 apples

Step-by-step explanation:

3+2+1 = 6 and 6 × 2 is 12 therefore half of the fruit is 6 so six apples (if that makes sense HAHA)

Mskskdkskekekdbsn nkfjrjrmrnrrr

A garden hose fills a 2-gallon bucket in 5 seconds. The number of gallons, g, is proportional to the number of seconds, t, that the water is running. Select all the equations that represent the relationship between g and t. A g= 0.4t
B t= 0.4G
C g=2.5t
D t=2.5g
E g= 2/5 t

The correct options are (A), (D) and (E).

### What is a linear equation?

A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.

It can be represented as a straight line on a graph.

Given that,

The time taken to fill 2 gallon bucket is 5 seconds.

Suppose the number of gallons be g.

And, the time in seconds is t.

The given options are considered one by one for the given case as,

(A) g = 0.4 t

Substitute g = 2 and t =5 in the above expression to get,

LHS = 2

RHS = 0.4 × 5

= 2

Since LHS = RHS, the given option represent the proportional relationship.

(B) t= 0.4g

Substitute g = 2 and t =5 in the above expression to get,

LHS = 5

RHS = 0.4 × 2

= 0.8

Since LHS ≠ RHS, the given option does not represent the proportional relationship.

(C) g=2.5t

Substitute g = 2 and t =5 in the above expression to get,

LHS = 2

RHS = 2.5 × 5

= 12.5

Since LHS ≠ RHS, the given option does not represent the proportional relationship.

(D)  t = 2.5g

Substitute g = 2 and t =5 in the above expression to get,

LHS = 5

RHS = 2.5 × 2

= 5

Since LHS = RHS, the given option represents the proportional relationship.

(E)  g= 2/5 t

Substitute g = 2 and t =5 in the above expression to get,

LHS = 2

RHS = 2/5 × 5

= 2

Since LHS = RHS, the given option represents the proportional relationship.

Hence, the correct relationship is represented by options (A), (D) and (E).

To know more about linear equation click on,

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I beleive it should be

A. g = 0.4t

And

D. t = 2.5g

Sorry if i'm wrong though! Let me know if is correct!

A flower delivery driver is 8 1/2 miles west of a city's zoo when she receives a call to pick up flowers from the flower store. The flower store is 14.35 miles east of the zoo. Assume the driver takes the most direct route to the flower store. How will the driver drive to the flower store? Select from the drop-down menus to correctly complete the statement. The driver will drive Choose... miles Choose... .

Step-by-step explanation:

Took the test and got a 100%

Step-by-step explanation:

if she starts out 8.5 mile WEST of a zoo, and has to go 14.35 miles EAST of the zoo, then add both of those numbers, and you get, 22.85 miles

-3-[(6+3)+(-5-18)]

11

Step-by-step explanation:

There are three workstations available having steady-state probabilities of 0.99, 0.95, 0.85 of being available on demand. What is the probability that at least two of the three will be available at any given time?

99.065% probability that at least two of the three will be available at any given time.

Step-by-step explanation:

We have these following probabilities:

99% probability of the first workstation being available

95% probability of the second workstation being available

85% probability of the third workstation being avaiable

Two being available:

We can have three outcomes

First and second available, third not. So

0.99*0.95*0.15 = 0.141075

First and third available, second not. So

0.99*0.05*0.85 = 0.042075

Second and third available, first not. So

0.01*0.95*0.85 = 0.008075

P(2) = 0.141075 + 0.042075 + 0.008075 = 0.191225

Three being available:

P(3) = 0.99*0.95*0.85 = 0.799425

What is the probability that at least two of the three will be available at any given time?

P = P(2) + P(3) = 0.191225 + 0.799425 = 0.99065

99.065% probability that at least two of the three will be available at any given time.

The probability that at least two out of the three workstations are available is 0.967.

### Explanation:

We can find the probability that at least two out of the three workstations are available using the concept of complementary events. The probability of at least two workstations being available is equal to 1 minus the probability of none or only one workstation being available.

Let's calculate the probability of none or only one workstation being available:

Probability of none being available: 0.01 * 0.05 * 0.15 = 0.00075
Probability of only one being available: (0.99 * 0.05 * 0.15) + (0.01 * 0.95 * 0.15) + (0.01 * 0.05 * 0.85) = 0.03225

Now, subtracting this from 1:

1 - (0.00075 + 0.03225) = 0.967

Therefore, the probability that at least two out of the three workstations are available at any given time is 0.967.

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3. (03.06) Choose the point-slope form of the equation below that represents the line that passes through the point (6, -3) and has a slope of 1/2​

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

where

m is the slope

( x1 , y1) is the point

From the question we have the final answer as

Hope this helps you