Question

1. Assume the random variable X represents the concentration of bacteria in a contaminated liquid, and that X is normally distributed with a mean µ=250 ppm and a standard deviation σ=70 ppm. Compute the approximate probability that Danielle would randomly select a container with a reading greater than 140 ppm.

Now, suppose that the value of the standard deviation was smaller, 40 ppm instead of 70 ppm. What would this tell us about the bacteria concentration in randomly selected container?

A. The graph would be more spread out.

B. There would be a higher probability of obtaining an extreme value.

C. The bacteria themselves would be smaller.

D. The various concentration values would be less variable.

Answer #1

Problem 7
Suppose you have a random variable X that represents the
lifetime of a certain brand of light bulbs. Assume that the
lifetime of light bulbs are approximately normally distributed with
mean 1400 and standard deviation 200 (in other words X ~ N(1400,
2002)).
Answer the following using the standard normal distribution
table:
Approximate the probability of a light bulb lasting less than
1250 hours.
Approximate the probability that a light bulb lasts between 1360
to 1460 hours.
Approximate...

Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X>4), n=7, p=0.4
Find the standard deviation of the following data. Round your
answer to one decimal place.
x
1
2
3
4
5
6
P(X=x)
0.1
0.1
0.2
0.1
0.2
0.3

1. Random Variable: The variable X represents the number of
goals scored by the soccer team Liverpool FC during all
competitions of the 2018- 2019 season.
X: 0, 1, 2, 3, 4, 5
P(X): 0.13, 0.25, 0.23, 0.17, 0.17, 0.05
a. Does the above table represent a probability distribution for
the variable X? Explain.
b. Calculate the mean value for the variable X.
c. What is the probability that they score 2 or more goals for a
given game during...

1. (6 pts) Let x be a random variable that represents
the length of time it takes a student to write a term paper for Dr.
Adam’s sociology class. After interviewing many students, it was
found that x has an approximate normal distribution with mean = 6.8
hours and standard deviation = 2.1 hours.
Convert the x interval x 4 to a standard z
interval.
Convert the z-score interval 0 ≤ ? ≤ 2 to a raw score x
interval.

In the following probability distribution, the random variable
x represents the number of activities a parent of a
6th to 8th-grade student is involved in. Complete parts (a)
through (f) below.
x
0
1
2
3
4
P(x)
0.395
0.075
0.199
0.195
0.136
(a) Verify that this is a discrete probability
distribution.
This is a discrete probability distribution because the sum of
the probabilities is ___and each probability is ___ (Less than or
equal to 1; Greater than or equal...

assume the random variable x is normally distributed
with mean 80 and standard deviation 4. Find the indicated
Probability P (70<×<76)

1) The random variable X represents the number of girls
in a family of 6 children. Assuming that the event of having boys
and girls are equally likely. Construct the discrete probability
distribution for the random variable X and plot your results. For
the number of girls, determine the expected mean and standard
deviation.

Three students answer a true-false question on a test randomly.
A random variable x represents the number of answers of true among
the three students, taking on the value 0, 1, 2, or 3.
(a) Find the frequency distribution for x.
(b) Find the probability distribution for x.
For the same random variable x as the previous problem, find the
following:
(a) The expected value (b) The variance (c) The standard
deviation

Assume a normal random variable, X, with mean 90 and standard
deviation 10. Find the probability that a randomly chosen value of
X is less than 95. Find the probability that a randomly chosen
value of X is between 60 and 100. Find the 97th percentile of the X
distribution (i.e., find the value x such that P(X<x)=0.97).
Find the probability that a randomly chosen value of X is greater
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Assume that individual daily wages of taxi drivers are described
as a random variable (X) that is normally distributed with
parameters (µ = 85, σ = 20). A sample of n = 4 drivers was selected
at random and Y = X¯ represents the sample mean, Y = X¯ = 1/4 · [X1
+ X2 + X3 + X4]
1. Find the chance that sample average (Y ) would be at least 70
and not exceeding 90
2. Evaluate probability...

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