What probability expression is equivalent to P( / z / > 1.96)?
1 answer:
You might be interested in
After applying <em>algebraic</em> analysis we find the <em>right</em> choices for each case, all of which cannot be presented herein due to <em>length</em> restrictions. Please read explanation below.
<h3>How to analyze rational functions</h3>
In this problem we have a rational function, whose features can be inferred by algebraic handling:
Holes - x-values that do not belong to the domain of the <em>rational</em> function:
x³ + 8 · x² - 9 · x = 0
x · (x² + 8 · x - 9) = 0
x · (x + 9) · (x - 1) = 0
x = 0 ∨ x = - 9 ∨ x = 1
But one root is an evitable discontinuity as:
y = (9 · x² + 81 · x)/(x³ + 8 · x² - 9 · x)
y = (9 · x + 81)/(x² + 8 · x - 9)
Thus, there are only two holes. (x = - 9 ∨ x = 1) Besides, there is no hole where the y-intercept should be.
Vertical asymptotes - There is a <em>vertical</em> asymptote where a hole exists. Hence, the function has two vertical asymptotes.
Horizontal asymptotes - <em>Horizontal</em> asymptote exists and represents the <em>end</em> behavior of the function if and only if the grade of the numerator is not greater than the grade of the denominator. If possible, this assymptote is found by this limit:
y = 0
The function has a horizontal asymptote.
x-Intercept - There is an x-intercept for all x-value such that numerator is equal to zero:
9 · x + 81 = 0
x = - 9
There is a x-intercept.
Lastly, we have the following conclusions:
- How many holes? 2
- One <em>horizontal</em> asymptote along the line where y always equals what number: 0
- This function has x-intercepts? True
- One <em>vertical</em> asymptote along the line where x always equals what number: 1
- There is a hole where the y-intercept should be? False
To learn more on rational functions: brainly.com/question/27914791
#SPJ1
Complete question is;
After examining daily receipts over the past year, it was found that the green parrot italian restaurant has been grossing over $2200 a day for about 85% of it's business days. Using this as a reasonably accurate measure, find the probability that the green parrot will gross over $2200:
A. At least 5 of the next 7 business days.
B. at least 5 of the next 10 business days.
C. less than 3 of the next 5 business days.
d. Exactly 7 of the next 10 business days
e. At least 1 of the next 5 business days.
Answer:
A) P(X ≥ 5) = 0.9262
B) P(X ≥ 5) = 0.9986
C) P(X ≤ 2) = 0.0266
D) P(X = 7) = 0.1298
E) P(X ≥ 1) = 0.9999
Step-by-step explanation:
This is a binomial probability distribution problem and as such we will use the formula;
P(X = k) = C(n, k) × p^(k) × (1 - p)^(n - k)
A. At least 5 of the next 7 business days will be;
P (X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7)
P(X = 5) = C(7, 5) × 0.85^(5) × (1 - 0.85)^(7 - 5)
P(X = 5) = 0.20965
P(X = 6) = C(7, 6) × 0.85^(6) × (1 - 0.85)^(7 - 6)
P(X = 6) = 0.396
P(X = 7) = C(7, 7) × 0.85^(7) × (1 - 0.85)^(7 - 7)
P(X = 7) = 0.320577
Thus;
P(X ≥ 5) = 0.20965 + 0.396 + 0.320577
P(X ≥ 5) = 0.9262
B. Probability of at least 5 of the next 10 business days will be;
P(X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
From online binomial calculator attached, we can see that the answer is;
P(X ≥ 5) = 0.9986
C. Probability of less than 3 of the next 5 business days will be;
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
From online binomial calculator attached, we can see that the answer is;
P(X ≤ 2) = 0.0266
D. Probability of exactly 7 of the next 10 business days will be;
P(X = 7) = C(10, 7) × 0.85^(7) × (1 - 0.85)^(10 - 7)
P(X = 7) = 0.1298
e. Probability of at least 1 of the next 5 business days will be;
P(X ≥ 1) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
From third image attached using online binomial calculator, we have;
P(X ≥ 1) = 0.9999
