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Let random variable SS represent the age of the attendees at a local concert. The following histogram shows the probability distribution of the random variable SS.

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7 votes

Answer:

5. No, the distribution is skewed to the left with a mean age greater than 36.

Explanation:

The problem is presented in the photo below. It says the following:

Let random variable S represent the age of the attendees at a local concert. The following histogram shows the probability distribution of the random variable S. Alfonso claims that the distribution of S is symmetric with a mean age of 36. Does the histogram supports Alfonso's claim.

  1. Yes, the distribution is symmetric with a mean age of 36.
  2. No, the distribution is skewed to the right with a mean age of 36.
  3. No, the distribution is skewed to the right with a mean age greater than 36.
  4. No, the distribution is skewed to the left with a mean age of 36.
  5. No, the distribution is skewed to the left with a mean age greater than 36.

Consider the given histogram at the photo below. it is an left-skew histogram , since it has a long tail to the left side.

We need to estimate the mean of the given data. To do so, we need to multiply each class midpoint with its probability, and sum them.

For example, for the first one, the midpoint is 32 and the probability is 0.03 (read the value on the y-axis). For, the second one, the midpoint is 33 and the probability is 0.04, for the third the midpoint is 34 and the probability is 0.05, and so on. All needed values are presented below.

  1. midpoint = 32, probability= 0.03
  2. midpoint = 33, probability = 0.04
  3. midpoint = 34, probability = 0.05
  4. midpoint = 35, probability = 0.1
  5. midpoint = 36, probability =0.11
  6. midpoint = 37, probability = 0.13
  7. midpoint = 38, probability = 0.2
  8. midpoint = 39, probability = 0.09

Therefore, we obtain


\mu = 0.03 \cdot 32 + 0.04 \cdot 33 + 0.05\cdot 34 + 0.10 \cdot 35 + 0.11 \cdot 36 + 0.13 \cdot 37 + 0.25 \cdot 38 + 0.20 \cdot 39 + 0.09 \cdot 40

which yields


\mu = 37.15

Therefore, this histogram is left-skewed with mean greater than 36.

Let random variable SS represent the age of the attendees at a local concert. The-example-1
User Hemant Kumar
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