For this case we must find the inverse of the following function:
Then, we follow the steps:
We change by y:
We exchange the variables:
We clear the variable "y":
We change y for
Answer:
Write the unit rate for the situation. $54.00 for 3 tickets
2 answers:
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Answer:
a) Range = 1.39
b) the sample variance is 0.1597
c) the sample standard deviation is 0.3996
Step-by-step explanation:
Given the data in the question;
a) Find the range.
To determine the range, we simple subtract the smallest value from the largest value. i.e
Range = largest value - smallest value
from data set; our smallest is 0.53 while our largest value is 1.92
so
Range = 1.92 - 0.53 = 1.39
b) Find the sample variance.
To determine our variance, we use the following formula;
∑( -
)² / n - 1 = [ ∑
²/n-1 ] - [
(
)²]
where = ∑
/n
n is sample size = 14 so lets calculate ∑
∑ = 0.99 + 1.92 + 1.23 + 0.85 + 0.65 + 0.53 + 1.41 + 1.12 + 0.63 + 0.67 + 0.69 + 0.60 + 0.60 + 0.66
∑ = 12.55
∑² = 0.99² + 1.92² + 1.23² + 0.85² + 0.65² + 0.53² + 1.41² + 1.12² + 0.63² + 0.67² + 0.69² + 0.60² + 0.60² + 0.66²
∑² = 13.3253
so
our = ∑
/n = 12.55 / 14 = 0.8964
so our Variance will be;
= [ ∑²/n-1 ] - [
(
)²]
= [ 13.3253 / 14-1 ] - [ (0.8964)²]
= 1.025 - 0.8653
= 0.1597
Therefore, the sample variance is 0.1597
c) Find the sample standard deviation.
we know that standard deviation is the square root of variance;
standard deviation = √Variance
standard deviation = √0.1597
standard deviation = 0.3996
Therefore, the sample standard deviation is 0.3996
Answer:
(a) The probability you pass the exam is 0.0000501.
(b) The expected number of correct guesses is 7.5.
(c) The standard deviation is 2.372.
Step-by-step explanation:
We are given that you take a 30-question, multiple-choice test, in which each question contains 4 choices: A, B, C, and D. And you randomly guess on all 30 questions.
Since there is an assumption of only 1 correct choice out of 4 which means the above situation can be represented through binomial distribution;
where, n = number of trials (samples) taken = 30
r = number of success = at least 60%
p = probbaility of success which in our question is the probability
of a correct answer, i.e; p = = 0.25
Let X = Number of questions that are correct
So, X ~ Binom(n = 30 , p = 0.25)
(a) The probability you pass the exam is given by = P(X 18)
Because 60% of 30 = 18
P(X 18) = P(X = 18) + P(X = 19) +...........+ P(X = 29) + P(X = 30)
=
= 0.0000501
(b) The expected number of correct guesses is given by;
Mean of the binomial distribution, E(X) =
= = 7.5
(c) The standard deviation of the binomial distribution is given by;
S.D.(X) =
=
= = 2.372