Hi I know how to calculate standard deviation but am having trouble with questions the in the image. Please help.. Either 8 or 10 worked out would be a huge help.
Hi I know how to calculate standard deviation but am having trouble with questions the in the image. Please help.. Either 8 or 10 worked out would be a huge help.
Since 173 is the mean and standard deviation is 7.7 cm. Thus, One standard deviation to the left and right takes 68% (a rule) thus, 165.3-180.7 take 68% of all the students. Thus 32% below 165.3 or above 180.7 cm. Now the normal distribution is symettric thus, 16% below 165.3 and 16% aboce 180.7 cm. Look at the problem it say the taller 15% thus, approximately the taller 16% thus the range is approximately 180.7 cm.
Look at the hint to look for the lower part of normal distribution. This problem unlike the first requires you to move 2 standard deviations. This will take on 95% (a rule) thus, between .9-4.1 years are included in these 95%. Thus, 5% below .9 or above 4.1 years. But because the normal distribution is symettric thus, 2.5% below .9 years or above 4.1 years. The problem asks for the 2.5% thus the range is .9 years.
Let be the precentage (or probability) of all values between and .
There is a theorem (theorem-1) in statistics that if something is normal distributed and is the mean, and is the standard deviation then,
.
Also because (theorem-2) the normal distribution has symettrism we have that If Then, . The reason being, because excludes the first one and then diving by 2 is because of symettrism.
Now to do problem 2, the mean and the standard deviation is . By the above explanations and theorem-1 (because 2 standard deviations). Next, use theorem-2 thus, =2.5% which you where trying to find.
Thus the answer is .
Q.E.D.
8. If the school has a normal distribution of height , with mean andOriginally Posted by Arbitur
standard deviation , then:
,
has a standard normal distribution. The height of the beams is such that
will hit their heads, call this height .
Call the corresponding score , then:
,
So of scores exceed , or of scores are less than .
Now look up the value of which gives in a table
of the cumulative normal distribution, doing this gives .
The corresponding height (which will be the height of the beams) will be
the solution of:
,
which when we plug in the value of gives:
.
Thus all students taller than cm. will be affected.
RonL