Write the coordinates of the vertices after a reflection over the y-axis.

The service department of a luxury car dealership conducted research on the amount of time its service technicians spend on each

mart [117]

Answer:

Probability that the mean service time is between 1 and 2 hours is 0.96764.

Step-by-step explanation:

We are given that a systematic random sample of 100 service appointments has been collected.

The 100 appointments showed an average preparation time of 90 minutes with a standard deviation of 140 minutes.

Let $\bar X$ = sample mean service time

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = average preparation time = 90 minutes

$\sigma$ = standard deviation = 140 minutes

n = sample of appointments = 100

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, probability that the mean service time is between 60 and 120 minutes is given by = P(60 minutes < $\bar X$ < 120 minutes)

P(60 minutes < $\bar X$ < 120 minutes) = P( $\bar X$ < 120 min) - P( $\bar X$ $\leq$ 60 min)

P( $\bar X$ < 120 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{120-90}{\frac{140}{\sqrt{100} } }$ ) = P(Z < 2.14) = 0.98382

P( $\bar X$ $\leq$ 60 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{60-90}{\frac{140}{\sqrt{100} } }$ ) = P(Z $\leq$ -2.14) = 1 - P(Z < 2.14)

= 1 - 0.98382 = 0.01618

The above probability is calculated by looking at the value of x = 2.14 in the z table which has an area of 0.98382.

Therefore, P(60 min < $\bar X$ < 120 min) = 0.98382 - 0.01618 = 0.96764

7 0

4 years ago

A cars value starts at $32,000. After 1 year, it is worth $27,200. What is the decay factor?

notka56 [123]

Answer:

15% × 7 = 1.05

32,000 - 1.05 = 31,998.95

31,998.95 ‐‐‐‐‐> 31,999

$31,999

(If you don't need to simplify, the answer would be $31,998.95, but I did it just incase you do)

Step-by-step explanation:

7 0

3 years ago

Tej ran 2000 metres in 15mins. what was his average speed in km/h?

Deffense [45]

His average speed in kilometers per hour is 8

8 0

4 years ago

A video company charges a yearly membership fee plus a daily rental charge for a movie. The cost c, if renting a movie for a cer

elena-14-01-66 [18.8K]

Answer:

answer A

Step-by-step explanation:

3 0

3 years ago

a quadrilateral has 2 right angles. the measure of the third angle is 73, what is the measure of the forth angle?

hoa [83]

Answer: 107 degrees.

Step-by-step explanation:

A quadrilateral is defined as a 2-dimensional closed shape which has four sides and four vertices.

By definition the interior angles of a quadrilateral add up 360 degrees.

We know that this quadrilateral has 2 right angles (which are angles that measure 90 degrees) and we know that the measure of the third angle is 73 degrees.

Let be "x" the measure of the fourth angle.

Then you can write this expression:

$360\°=90\°+90\°+73\°+x$

And finally solve for "x":

$360\°=253\°+x$

$360\°-253\°=x$

$x=107\°$

5 0

3 years ago