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Archy [21]
3 years ago
8

The following histogram shows the relative frequencies of the heights, recorded to the nearest inch, of a population of women. T

he mean of the population is 64.97 inches, and the standard deviation is 2.66 inches.
One woman from the population will be selected at random.

Question 3
(c) The histogram displays a discrete probability model for height. However, height is often considered a continuous variable that follows a normal model. Consider a normal model that uses the mean and standard deviation of the population of women as its parameters.

(i) Use the normal model and the relationship between area and relative frequency to find the probability that the randomly selected woman will have a height of at least 67 inches. Show your work.

(ii) Does your answer in part (c-i) match your answer in part (a) ? If not, give a reason for why the answers might be different.

Question 4
(d) Let the random variable H represent the height of a woman in the population. P(H<60) represents the probability of randomly selecting a woman with height less than 60 inches. Based on the information given, the probability can be found using either the discrete model or the normal model.

(i) Give an example of a probability of H that can be found using the discrete model but not the normal model. Explain why.

(ii) Give an example of a probability of H that can be found using the normal model but not the discrete model. Explain why.

Mathematics
1 answer:
Airida [17]3 years ago
6 0

Answer:

The following histogram shows the relative frequencies of the height recorded to the nearest inch of population of women the mean of the population is 64.97 inches and the standard deviation is 2.66 inches

(a) Based on the histogram, what is the probability that the selected woman will have a height of at least 67 inches? Show your work

Answer:

0.22268

Step-by-step explanation:

z-score is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

(a) Based on the histogram, what is the probability that the selected woman will have a height of at least 67 inches? Show your work

At least means equal to or greater than 67 inches

z = 67 - 64.97/2.66

z = 0.76316

P-value from Z-Table:

P(x<67) = 0.77732

P(x>67) = 1 - P(x<67) = 0.22268

The probability that the selected woman will have a height of at least 67 inches is 0.22268

Step-by-step explanation:

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