7-7(5+x)-9x in simplified
1 answer:
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Answer:
(a) The probability that X is at most 30 is 0.9726.
(b) The probability that X is less than 30 is 0.9554.
(c) The probability that X is between 15 and 25 (inclusive) is 0.7406.
Step-by-step explanation:
We are given that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked. A random sample of 200 shafts is taken.
Let X = <u><em>the number among these that are nonconforming and can be reworked</em></u>
The above situation can be represented through binomial distribution such that X ~ Binom(n = 200, p = 0.11).
Here the probability of success is 11% that this much % of all steel shafts produced by a certain process are nonconforming but can be reworked.
Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).
So, the new mean of X, =
=
= 22
and the new standard deviation of X, =
=
= 4.42
So, X ~ Normal()
(a) The probability that X is at most 30 is given by = P(X < 30.5) {using continuity correction}
P(X < 30.5) = P( <
) = P(Z < 1.92) = <u>0.9726</u>
The above probability is calculated by looking at the value of x = 1.92 in the z table which has an area of 0.9726.
(b) The probability that X is less than 30 is given by = P(X 29.5) {using continuity correction}
P(X 29.5) = P(
) = P(Z
1.70) = <u>0.9554</u>
The above probability is calculated by looking at the value of x = 1.70 in the z table which has an area of 0.9554.
(c) The probability that X is between 15 and 25 (inclusive) is given by = P(15 X
25) = P(X < 25.5) - P(X
14.5) {using continuity correction}
P(X < 25.5) = P( <
) = P(Z < 0.79) = 0.7852
P(X 14.5) = P(
) = P(Z
-1.70) = 1 - P(Z < 1.70)
= 1 - 0.9554 = 0.0446
The above probability is calculated by looking at the value of x = 0.79 and x = 1.70 in the z table which has an area of 0.7852 and 0.9554.
Therefore, P(15 X
25) = 0.7852 - 0.0446 = 0.7406.
Answer:
From least to greatest it is -5/2, -2, then 1.7
Step-by-step explanation:
First by process of elimination, 1.7 is the only positive number, so it is the greatest number compared to the other two.
Now we are left with -2 and -5/2.
We can rewrite -2 as , as any number by itself itself is the number over 1.
Then we need to find the common denominator for both fractions, meaning they must share the same bottom number.
The 1 in the denominator can be multiplied by 2 to get a denominator of 2 , the same as the denominator for .
Since the denominator is multiplied by 2, the numerator also has to be multiplied by 2:
Now since both fractions share the same denominator, we can compare them by their numerators. 5 is greater than 4, but we must keep in mind that these are negative. The larger the negative number, the smaller the value.
So when comparing -4/2 and -5/2, -5/2 is smaller.
So our final answer from least to greatest is -5/2, -2, then 1.7