A variable that can have any value between two given value is known as continuous variable, while a variable have only integer values is a discrete variable
The correct values are;
(c) (i) The probability of a height of at least 67 is 0.2263
(ii) The answers do not match due to the difference between the discrete and normal probability models
(d) (i) A probability that can be found using the discrete model but not the normal model is P (H = 60)
The probability of an exact value using the normal distribution is zero
(ii) A probability that can be found using the normal model but not the discrete model is P(H = 56)
The value is for height of 56 inches is not given on the histogram and therefore
The reason the above selections are correct is follows:
(c) (i) Using the normal probability model, we have;
The mean = 64.27 inches, the standard deviation = 2.66 inches
The z-score for the height of 67 inches is given as follows;
[tex]z = \mathbf{\dfrac{x - \mu}{\sigma}}[/tex]
Therefore, we have;
[tex]z = \dfrac{67 -64.97}{2.66} \approx 0.7632[/tex]
From the z-score table, the probability P(x < 67) = 0.7737
P(x > 67) = 1 - P(x < 67) = 1 - 0.7737 = 0.2263
The probability of a height of at least 67, by the normal model = 0.2263
(ii) Based on the histogram, we have;
The probability of at least 67 = The area of the bars equal to and larger than 67 = (0.11 + 0.07 + 0.05 + 0.02 + 0.01 + 0.01) × 1 = 0.27
The probability of a height of at least 67 = 0.27
The answer in part (c-i) and the answer in part (a) using the histogram do not match
The reason they do not match is that the normal model used in part c is
based on normal probability, which focuses on future events, using the
normal model which is a continuous probability model, while the value of
probability calculated using the histogram is based on the relative
frequency, which focuses on historical values, based on the discrete model
(d) (i) An example of a probability that can be found using the discrete model but not the normal model is the probability that the height of a woman is a discreet single value such as 65 inches
Therefore, using the discreet model, we have;
P(H = 65) = 0.18
Using the continuous model, we have;
P(H = 65) = 0
This is so because the continuous model is given by the area under the curve, which for a single value is infinitesimally small
(ii) An example of a probability that can be found using the normal model but not the discrete model is the probability of the height of a woman selected is 56 inches, P(H = 56) is not given in the histogram
Learn more about discrete and normal probability distributions here:
https://brainly.com/question/6476990
