Thickness measurements of ancient prehistoric native american pot shards discovered in a hopi village are approximately normally distributed, with a mean of 4.5 millimeters (mm) and a standard deviation of 1.5 mm. for a randomly found shard, find the following probabilities. (round your answers to four decimal places.)

(a) the thickness is less than 3.0 mm

(b) the thickness is more than 7.0 mm

(c) the thickness is between 3.0 mm and 7.0 mm

a) 0.1587 (or 15.87%)

b) 0.0478 (or 4.78%)

c) 0.7935 (or 79.35%)

Step-by-step explanation:

Find the following probabilities:

(a) the thickness is less than 3.0 mm

We need to find the area under the Normal curve with a mean of 4.5 mm and a standard deviation of 1.5 mm to the left of 3 mm

We can do that with the help of a calculator or a spreadsheet.

In Excel use

NORMDIST(3,4.5,1.5,1)

In OpenOffice Calc use  

NORMDIST(3;4.5;1.5;1)

and we get the value 0.1587 (or 15.87%)

(b) the thickness is more than 7.0 mm

Now we need the area to the right of 7 (1 - the area to the left of 7)

In Excel use

1-NORMDIST(7,4.5,1.5,1)  

In OpenOffice Calc use  

1-NORMDIST(7;4.5;1.5;1)

and we get the value 0.0478 (or 4.78%)

(c) the thickness is between 3.0 mm and 7.0 mm

We are looking for the area between 3 and 7

Since the area under the Normal equals 1, we have

Area to the left of 3 + Area between 3 and 7 + Area to the right of 7 = 1

Hence,  

0.1587 +  Area between 3 and 7 + 0.0478 = 1

and

Area between 3 and 7 = 1 - 0.1587 - 0.0478 = 0.7935 (or 79.35%)

54 km / hours

step-by-step explanation:

we need to convert seconds to hours

60 seconds = 1 minutes

60 minutes = 1hour

15 m         60 second   60 minutes

  * *         = 54000 meters/ hour

second     1 minute             1 hour

now we need to convert meters to km

1000 m = 1 km

54000 m       1 km

*   = 54 km / hours

hour               1000m

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step-by-step explanation: