The isosceles triangle theorem states that if two sides of a triangle are congruent, then the angles opposite those sides are __
1 answer:
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Suppose
At the same time, we can write
Note that (just reverse the sum). Let's pair the first terms of
and
, and the second, and the third, and so on:
Now, each grouped term in the sum on the right side adds to 151. There are 52 grouped terms on that same side (because there are 50 numbers in the range of integers 51-100, plus 50 and 101), which menas
But , as we pointed out, so
Answer:
46.18% of the items will weigh between 6.4 and 8.9 ounces.
Step-by-step explanation:
We are given that the weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.
<em>Let X = weight of items produced by a machine</em>
The z-score probability distribution for is given by;
Z = ~ N(0,1)
where, = mean weight = 8 ounces
= standard deviation = 2 ounces
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.
So, percentage of items that will weigh between 6.4 and 8.9 ounces is given by = P(6.4 < X < 8.9) = P(X < 8.9 ounces) - P(X 6.4 ounces)
P(X < 8.9) = P( <
) = P(Z < 0.45) = 0.67364 {using z table}
P(X 70) = P(
) = P(Z
-0.80) = 1 - P(Z < 0.80)
= 1 - 0.78814 = 0.21186
<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.45 and x = 0.80 in the z table which has an area of </em>0.67364<em> and </em>0.78814<em> respectively.</em>
Therefore, P(6.4 < X < 8.9) = 0.67364 - 0.21186 = 0.4618 or 46.18%
<em>Hence, 46.18% of the items will weigh between 6.4 and 8.9 ounces.</em>