In a recent survey, 35 percent indicated chocolate was their favorite flavor of ice cream. Suppose we select a sample of ten people and ask them to name their favorite flavor of ice cream.



(b)
What is the probability exactly four of those in the sample name chocolate? (Do not round intermediate values. Round your answer to 4 decimal places.)



(c)
What is the probability four or more name chocolate? (Round intermediate values to 4 decimal places. Round your answer to 4 decimal places.)

a. E(x)=np=(10)(0.35)=3.5

b. p(x=4)=10C4(0.35)^4(1-0.35)^6
=0.2376
c.

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c jawabannya apa ya?

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(b) To calculate the probability of exactly four people in the sample naming chocolate as their favorite flavor, we can use the binomial probability formula. The formula can be written as:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

Where:
n is the sample size (10 in this case)
k is the number of people naming chocolate (4 in this case)
p is the probability of naming chocolate as their favorite flavor (0.35)

Using this formula, we can calculate the probability as follows:

P(X = 4) = (10 choose 4) * 0.35^4 * (1 - 0.35)^(10 - 4)

P(X = 4) = (10! / (4! * (10 - 4)!)) * 0.35^4 * (1 - 0.35)^6

P(X = 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) * 0.35^4 * (0.65)^6

P(X = 4) = 0.250822 * 0.119025 * 0.305175

P(X = 4) ≈ 0.010822 (rounded to 4 decimal places)

Therefore, the probability of exactly four people in the sample naming chocolate as their favorite flavor is approximately 0.0108.

(c) To calculate the probability of four or more people naming chocolate, we need to sum up the probabilities of four, five, six, seven, eight, nine, and ten people naming chocolate.

P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

We have already calculated P(X = 4), so we can calculate the probabilities for the other values of k using the same formula.

P(X = 5) = (10 choose 5) * 0.35^5 * (1 - 0.35)^(10 - 5)
P(X = 6) = (10 choose 6) * 0.35^6 * (1 - 0.35)^(10 - 6)
P(X = 7) = (10 choose 7) * 0.35^7 * (1 - 0.35)^(10 - 7)
P(X = 8) = (10 choose 8) * 0.35^8 * (1 - 0.35)^(10 - 8)
P(X = 9) = (10 choose 9) * 0.35^9 * (1 - 0.35)^(10 - 9)
P(X = 10) = (10 choose 10) * 0.35^10 * (1 - 0.35)^(10 - 10)

After calculating these probabilities, we can sum them up to find P(X ≥ 4), rounding to 4 decimal places.

To calculate the probability in this scenario, you need to use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where:
- n is the number of trials (sample size),
- k is the number of successful outcomes (number of people selecting chocolate),
- p is the probability of success (probability of selecting chocolate),
- (n choose k) is the binomial coefficient, which represents the number of ways to choose k successful outcomes from n trials.

In this case, n = 10 (sample size), p = 0.35 (probability of selecting chocolate), and k = 4 (exactly four people out of the sample selecting chocolate).

(b) To find the probability that exactly four people in the sample name chocolate:
P(X = 4) = (10 choose 4) * (0.35^4) * (0.65^6)
= (10! / (4! * (10 - 4)!)) * (0.35^4) * (0.65^6)
= (10! / (4! * 6!)) * (0.35^4) * (0.65^6)
= (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) * (0.35^4) * (0.65^6)
= 210 * 0.1500625 * 0.2522342
= 7.5247375

So, the probability of exactly four people in the sample naming chocolate is approximately 0.7525.

(c) To find the probability that four or more people in the sample name chocolate, you need to calculate the cumulative probability for k = 4, 5, 6, ..., 10:
P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) + ... + P(X = 10)

You can calculate each individual probability using the formula from part (b) and then sum them up.

P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) + ... + P(X = 10)
= 0.7525 + P(X = 5) + P(X = 6) + ... + P(X = 10)

You can compute each probability using the same formula as in part (b) and sum them up to get the final result.

0.44