25 POINTS WORTH
2 answers:
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Answer:
(a) P(X=1) = 0.3079
(b) P(X≥1) = 0.3965
(c) P(X≥2) = 0.0886
(d) P(X≤1.9) = 0.9114
(e) Expected no. of hours = 3.594 hours
Step-by-step explanation:
We have,
p = 0.02
n = 25
q = 1-p
q = 0.98
We will use the binomial distribution formula to solve this question. The formula is:
P(X=x) = ⁿCₓ pˣ qⁿ⁻ˣ
where n = total no. of trials
x = no. of successful trials
p = probability of success
q = probability of failure
Let X be the number of students who received a special accommodation.
(a) P(X=1) = ²⁵C₁ (0.02)¹ (0.98)²⁵⁻¹
= 25*0.02*0.61578
P(X=1) = 0.3079
(b) P(X≥1) = 1 - P(X<1)
= 1 - P(X=0)
= 1 - (²⁵C₀ (0.02)⁰ (0.98)²⁵⁻⁰)
= 1 - 0.6035
P(X≥1) = 0.3965
(c) P(X≥2) = 1 - P(X<2)
= 1 - [P(X=0) + P(X=1)]
= 1 - (0.6035 + 0.3079)
= 1 - 0.9114
P(X≥2) = 0.0886
(d) The probability that the number among 25 who received a special accommodation is within 2 standard deviations of the expected number of accommodations. This means we need to compute the probability P(X-μ≤2σ). For this we need to calculate the mean and standard deviation of this distribution.
μ = np = (25)*(0.02) = 0.5
σ = = √(25)*(0.02)*(0.98) = √0.49 = 0.7
P(X-μ≤2σ) = P(X - 0.5≤ 2(0.7)) = P(X≤ 1.4 + 0.5) = P(X≤1.9)
P(X≤1.9) = P(X=0) + P(X=1)
= 0.6035 + 0.3079
P(X≤1.9) = 0.9114
(e) Student who does not receive a special accommodation i.e. X=0 is given 3 hours for the exam whereas an accommodated student P(X>0) is given 4.5 hours. The expected average number of hours given on the exam can be calculated as:
Expected no. of hours = ∑x*P(x)
= 3*P(X=0) + 4.5*P(X>0)
= 3*0.6035 + 4.5(1 - P(X≤0))
= 1.8105 + 4.5(1 - 0.6035)
= 1.8105 + 1.78425
Expected no. of hours = 3.594 hours
Answer:
Step-by-step explanation:
As per the question statement, a₁ is -6.25 and common ratio (r) is 1.25.
Therefore, the six terms of finite sequence would be as per the following equation . Thus, the series would be
- a1 = -6.25
- a2 = -6.25*r = -6.25*(1.25) = -7.8125
- a3 = -6.25*r^2 = -6.25*(1.25)^2 = -9.765625
- a4 = -6.25*r^3 = -6.25*(1.25)^3 = -12.20703125
- a5 = -6.25*r^4 = -6.25*(1.25)^4 = -15.2587890625
- a6 = -6.25*r^5 = -6.25*(1.25)^5 = -19.073486328125
So the points on the graph will be on following points,
(1, -6.25), (2, -7.8125), (3, -9.765625), (4, -12.20703125), (5, -15.2587890625), (6, -19.073486328125).
The graph would look like as attached.
