Question

1a.Based on an analysis of sample data, an article proposed the
pdf * f*(

(a) What is the probability that waiting time is at most 2 sec? More than 2 sec?

at most 2 sec |
(P ≤ 2)X |
= | ||

more than 2 sec |
(P > 2)X |
= |

(b) What is the probability that waiting time is between 6 and 7 sec?

1b)Suppose the reaction temperature *X* (in °C) in a
certain chemical process has a uniform distribution with
* A* = −9 and

Compute * P*(−6 ≤

Please help thank you very much.

Answer #1

1b)0.78

Based on an analysis of sample data, an article proposed the
pdf
f(x) =
0.65e−0.65(x −
1)
when
x ≥ 1
as a model for the distribution of
X = time (sec)
spent at the median line. (Round your answers to three decimal
places.)
(a) What is the probability that waiting time is at most 3 sec?
More than 3 sec?
at most
3 sec
P(X ≤ 3)
=
more
than 3 sec
P(X > 3)
=
(b)...

Let X denote the amount of space occupied by an article
placed in a 1-ft3 packing container. The pdf of
X is below.
f(x) =
90x8(1 − x)
0
< x < 1
0
otherwise
(a) Graph the pdf.
Obtain the cdf of X.
F(x) =
0
x < 0
x9(10−9x)
0 ≤ x ≤ 1
1
x > 1
Graph the cdf of X.
(b) What is P(X ≤ 0.65) [i.e., F(0.65)]?
(Round your answer to four...

An article in American Demographics claims that more than twice
as many shoppers are out shopping on the weekends than during the
week. Not only that, such shoppers also spend more money on their
purchases on Saturdays and Sundays! Suppose that the amount of
money spent at shopping centers between 4 p.m. and 6 p.m. on
Sundays has a normal distribution with mean $190 and with a
standard deviation of $20. A shopper is randomly selected on a
Sunday between...

1. Complete the PDF.
x
P(X =
x)
x · P(X =
x)
0
0.1
1
0.4
2
3
0.2
Part (a) Find the probability that X = 2.
Part (b) Find the expected value.
2. A school newspaper reporter decides to randomly survey 16
students to see if they will attend Tet (Vietnamese New Year)
festivities this year. Based on past years, she knows that 21% of
students attend Tet festivities. We are interested in the number of
students...

The time spent waiting in the line is approximately normally
distributed. The mean waiting time is 6 minutes and the standard
deviation of the waiting time is 1 minute. Find the probability
that a person will wait for more than 7 minutes. Round your answer
to four decimal places

Let X be a continuous random variable with the probability
density function f(x) = C x, 6 ≤ x ≤ 25, zero otherwise.
a. Find the value of C that would make f(x) a valid probability
density function. Enter a fraction (e.g. 2/5): C =
b. Find the probability P(X > 16). Give your answer to 4
decimal places.
c. Find the mean of the probability distribution of X. Give your
answer to 4 decimal places.
d. Find the median...

x
P(x)
0
0.25
1
0.05
2
0.15
3
0.55
Find the standard deviation of this probability distribution. Give
your answer to at least 2 decimal places

An article suggests the uniform distribution on the interval
(7.5, 20) as a model for depth (cm) of the bioturbation layer in
sediment in a certain region.
(a) What are the mean and variance of depth? (Round your
variance to two decimal places.)
mean
variance
(b) What is the cdf of depth?
F(x) =
0
x < 7.5
7.5 ≤
x < 20
1
20 ≤
x
(c) What is the probability that observed depth is at...

An article suggests the uniform distribution on the interval
(8.5, 21) as a model for depth (cm) of the bioturbation layer in
sediment in a certain region.
(a) What are the mean and variance of depth? (Round your
variance to two decimal places.)
mean
variance
(b) What is the cdf of depth?
F(x) =
0
x < 8.5
8.5 ≤
x < 21
1
21 ≤
x
(c) What is the probability that observed depth is at...

1.
Create a PDF table and calculate expected
value.
A friend offers you a game to play where you pay him $10. You
roll a fair 6-sided die. If the roll of a comes up as 1, 2, 3 he
pays you $5. If the roll is 4 or 5 he pays you $7 and if it is a 6
he pays you $20.
In words, define the random variable X. ?
Construct a PDF table.
If you play this...

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