The manager of a vacation resort believes that the ages of adult visitors to the resort can be modeled by a normal distribution.
The manager surveyed a random sample of 765 visitors and recorded their age. A summary of the responses is shown in the frequency table, where x represents the age of the visitor. a) Construct a histogram of the distribution of ages. (b) Write a few sentences to describe the distribution of ages of the adult visitors to the resort.
1 answer:
Step-by-step explanation:
(a) A histogram is like a bar graph, but with ranges instead of values.
(b) The distribution is approximately uniform, with slightly more people at the younger and older ends than in the middle.
(c) The ages do not appear to come from a normal distribution. Normal distributions are bell-shaped, tall in the middle and short on the sides.
You might be interested in
Answer:
(a) The probability density function of <em>X</em> is:
(b) The value of P (129 ≤ X ≤ 146) is 0.3462.
(c) The probability that a randomly selected flight between the two cities will be at least 3 minutes late is 0.4327.
Step-by-step explanation:
The random variable <em>X</em> is defined as the flight time between the two cities.
Since the random variable <em>X</em> denotes time interval, the random variable <em>X</em> is continuous.
(a)
The random variable <em>X</em> is Uniformly distributed with parameters <em>a</em> = 10 minutes and <em>b</em> = 154 minutes.
The probability density function of <em>X</em> is:
(b)
Compute the value of P (129 ≤ X ≤ 146) as follows:
Apply continuity correction:
P (129 ≤ X ≤ 146) = P (129 - 0.50 < X < 146 + 0.50)
= P (128.50 < X < 146.50)
Thus, the value of P (129 ≤ X ≤ 146) is 0.3462.
(c)
It is provided that a randomly selected flight between the two cities will be at least 3 minutes late, i.e. <em>X</em> ≥ 128 + 3 = 131.
Compute the value of P (X ≥ 131) as follows:
Apply continuity correction:
P (X ≥ 131) = P (X > 131 + 0.50)
= P (X > 131.50)
Thus, the probability that a randomly selected flight between the two cities will be at least 3 minutes late is 0.4327.