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Novay_Z [31]
3 years ago
12

64% of US adults have very little confidence in newspapers you randomly select 10 US adults find the probability that the number

of US adults who have very little confidence in newspapers is a exactly 5 be at least six and C less than four
Mathematics
1 answer:
9966 [12]3 years ago
5 0

Answer:

A) 0.1636

B) 0.7292

C) 0.0305

Step-by-step explanation:

This is a binomial probability distribution question that follows;

P(X = x) = nCx × p^(x) × q^(n - x)

In this case, p = 64% = 0.64

q = 1 - p = 1 - 0.64 = 0.36

Thus;

A) P(exactly 5) = P(5) = 10C5 × 0.64^(5) × 0.36^(10 - 5) = 0.1636

B) P(at least 6) = P(x ≥ 6) = P(6) + P(7) + P(8) + P(9) + P(10)

P(6) = 10C6 × (0.64^(6)) × (0.36^(10 - 6)) = 0.2424

P(7) = 10C7 × (0.64^(7)) × (0.36^(10 - 7)) = 0.2462

P(8) = 10C8 × (0.64^(8)) × (0.36^(10 - 8)) = 0.1642

P(9) = 10C9 × (0.64^(9)) × (0.36^(10 - 9)) = 0.0649

P(10) = 10C10 × (0.64^(10)) × (0.36^(10 - 10)) = 0.0115

Thus;

P(x ≥ 6) = 0.2424 + 0.2462 + 0.1642 + 0.0649 + 0.0115

P(x ≥ 6) = 0.7292

C) P(x < 4) = P(0) + P(1) + P(2) + P(3)

From online binomial probability calculator, we have;

P(x < 4) = 0.0305

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Deposited amount = $14.

Rate of interest =  2.7%

In decimals 2.7 could be written by dividing 2.7 by 100, we get

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Interest earned each year = 2.7% of $14 = 0.027*14 = $0.378.

We can make a table to balance by after each year.

First year balance: First year interest + Deposited amount = 0.378 +14 = $14.378.

Second year balance: Second year interest + Deposited amount = 2*0.378 +14 = 0.756+ 14 = $14.756.

Third year balance: Third year interest + Deposited amount = 3*0.378 +14 = 1.134+ 14 = $15.134.

We get four coordinates to graph A(0,14), B(1, 14.378) , C(2, 14.756) and D(3, 15.134).

Plotting those coordinates of the points A, B, C and D on the graph.



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