Answer:
0.1507 or 15.07%.
Step-by-step explanation:
We have been given that the manufacturing of a ball bearing is normally distributed with a mean diameter of 22 millimeters and a standard deviation of .016 millimeters. To be acceptable the diameter needs to be between 21.97 and 22.03 millimeters.
First of all, we will find z-scores for data points using z-score formula.
, where,
z = z-score,
x = Sample score,
= Mean,
= Standard deviation.
Let us find z-score of data point 22.03.
Using probability formula 
, we will get:
Therefore, the probability that a randomly selected ball bearing will be acceptable is 0.1507 or 15.07%.
Step-by-step explanation:
15 : 40
Both have table of 5 in common
5 : 8
1/2 is equivalent to 2/4 because,
2(1/2) = 2/4
So as you can see if you multiply the numerator(top) and the denominator(bottom) by the same number, you get an equivalent fraction! In my example you can see that I multiplied both by 2.
Use the geometric mean for right triangles here. Like this
. Cross multiply to get
, and
. That simplifies down to
. Pull out the 9 as a perfect square of 3 and you're left with
, first choice above.
Answer:
Mean for a binomial distribution = 374
Standard deviation for a binomial distribution = 12.97
Step-by-step explanation:
We are given a binomial distribution with 680 trials and a probability of success of 0.55.
The above situation can be represented through Binomial distribution;
where, n = number of trials (samples) taken = 680 trials
r = number of success
p = probability of success which in our question is 0.55
So, it means X <em>~ </em>
<em><u>Now, we have to find the mean and standard deviation of the given binomial distribution.</u></em>
- Mean of Binomial Distribution is given by;
E(X) = n 
p
So, E(X) = 680 0.55 = 374
- Standard deviation of Binomial Distribution is given by;
S.D.(X) = 
= 
= 
= 12.97
Therefore, Mean and standard deviation for binomial distribution is 374 and 12.97 respectively.
