C - Two pairs of opposite sides are congruent
Answer:
Step-by-step explanation:
Domain of a function is a set of x-values (input values) for which the function is defined.
Range of a function is a set of y-values (output values) for the given set of input values.
7). Domain → (-∞, ∞)
Range → (-∞, ∞)
8). Domain → (-∞, ∞)
Range → [-2, ∞)
9). Domain → [-2, 2]
Range → [-3, 3]
10). Domain → (-∞, ∞)
Range → [-1, 1]
Answer:
In this case we use the Poisson distribution because we are talking about the occurrence of an event (number of tracks) over a specified interval (in this case an area interval).
The probability of the event occurring x times over an interval is:
P(x) = nˣ × e⁻ⁿ ÷ x!
where n is the mean.
a) P(7) = 6⁷ × e⁻⁶ ÷ 7! = 0.1376
b) P(x ≥ 3) = 1 - P(x < 3) = 1 - P(2) - P(1) - P(0)
P(2) = 6² × e⁻⁶ ÷ 2! = 0.0446
P(1) = 6¹ × e⁻⁶ ÷ 1! = 0.0149
P(0) = 6⁰ × e⁻⁶ ÷ 0! = 0.0025
P(x ≥ 3) = 0.9380
c) P(2 < x < 7) = P(3) + P(4) + P(5) + P(6) = 0.0892 + 0.1339 + 0.1606 + 0.1606 = 0.5443
d) The mean is going to be 6.
e) The standard deviation is √n = √6 = 2.4
Answer:
90% confidence interval for the population mean is between a lower limit of $92.18 and an upper limit of $107.82.
Step-by-step explanation:
Confidence interval for a population mean is given as mean +/- margin of error (E)
mean = $100
sd = $25.20
n = 30
degree of freedom = n-1 = 30-1 = 29
confidence level (C) = 90% = 0.9
significance level = 1 - C = 1 - 0.9 = 0.1 = 10%
critical value (t) corresponding to 29 degrees of freedom and 10% significance level is 1.699
E = t×sd/√n = 1.699×25.20/√30 = $7.82
Lower limit of population mean = mean - E = 100 - 7.82 = $92.18
Upper limit of population mean = mean + E = 100 + 7.82 = $107.82
90% confidence interval is ($92.18, $107.82)
