Question
In: Statistics and Probability
The number of hours a battery lasts before failing follows an exponential distribution with a mean...
The number of hours a battery lasts before failing follows an exponential distribution with a mean of μ = 24.5 hours and a standard deviation of 10 hours. Eric buys a pack of 64 batteries. Find the probability that the average number of hours a battery lasts is 21 hours or less.
a. 0.0026
b. 0.9974
c. 0.3632
d. -2.80
Solve the problem and show all your work below. Draw appropriate pictures!
Solutions
Expert Solution
Solution :
Given that,
mean = 
= 24.5
standard deviation = 
= 10
n = 64
= 24.5
= /
n = 10/
64=1.25
P(
<21 ) = P[(
-
) /
< (21-24.5) /1.25 ]
= P(z <-2.8 )
Using z table
= 0.0026
probability= 0.0026
orchestra answered 2 years agoRelated Solutions
An important feature of tablets is battery life, the number of hours before the battery needs...
An important feature of tablets is battery life, the number of
hours before the battery needs to be recharged. The data shown in
the table below contain the battery life of 10 WiFi-only and 10
3G/4G/WiFi 9- through 12-inch tablets. Complete parts (a)
through (c).
WiFi-only
3G/4G/WiFi
4444
2525
3030
3535
4242
7070
5050
5454
5050
5555
5050
2121
3535
5959
5555
2525
3535
3232
4141
6666
a. Assuming that the population variances from both types of
tablets are equal,...
An important feature of tablets is battery life, the number of hours before the battery needs...
An important feature of tablets is battery life, the number of
hours before the battery needs to be recharged. The following table
shows the battery life of 12 WiFi-only and 7 3G/4G/WiFi 9-through
12-inch tablets:
WiFi Only
3G/4G+WiFi
12.40
11.70
10.60
11.40
11.50
10.70
12.60
11.50
8.00
11.30
10.90
11.60
11.60
8.90
10.00
10.90
8.90
9.50
10.50
Assuming that the population variances from both types of
tablets are equal, is there evidence of a difference in the means
battery life...
An important feature of tablets is battery life, the number of hours before the battery needs...
An important feature of tablets is battery life, the number of
hours before the battery needs to be recharged. The file Tablets
contains the battery life of 12 WiFi-only and 7 3G/4G/WiFi 9-
through 12-inch tablets. (Data extracted from “Ratings and rec-
ommendations: Tablets,” Consumer Reports, August 2013, p.
24.)
a. Assuming that the population variances from both types
of
tablets are equal, is there evidence of a difference in the
mean
battery life between the two types of tablets?...
An important feature of tablets is battery life, the number of hours before the battery needs...
An important feature of tablets is battery life, the number of
hours before the battery needs to be recharged. The data shown in
the table below contain the battery life of 10 WiFi-only and 10
3G/4G/WiFi 9- through 12-inch tablets.
WiFi-only
3G/4G/WiFi
48
26
35
40
44
65
52
51
60
52
48
23
38
51
56
25
36
31
50
66
a. Assuming that the population variances from both types of
tablets are equal, is there evidence of a...
The lifetime of a certain type of batteries follows an exponential distribution with the mean of...
The lifetime of a certain type of batteries follows an
exponential distribution with the mean of 12 hours.
a) What is the probability that a battery will last more than 14
hours? (Answer: 0.3114)
b) Once a battery is depleted, it is replaced with a new battery
of the same type. Assumingindependence between lifetimes of
batteries, what is the probability that exactly 2 batteries will be
depleted within 20 hours? (Answer: 0.2623)
c) What is the probability that it takes...
The distance between major cracks in a highway follows an exponential distribution with a mean of...
The distance between major cracks in a highway follows an
exponential distribution with a mean of 21 miles. Given that there
are no cracks in the first five miles inspected, what is the
probability that there is no major crack in the next 5 mile
stretch? Please enter the answer to 3 decimal places.
5) The lifetime of a certain type of batteries follows an exponential distribution with the mean...
5) The lifetime of a certain type of batteries follows an
exponential distribution with the mean of 12 hours.
a) What is the probability that a battery will last more than
14 hours?
b) Once a battery is depleted, it is replaced with a new
battery of the same type. Assuming independence between lifetimes
of batteries, what is the probability that exactly 2 batteries will
be depleted within 20 hours?
c) What is the probability that it takes less than...
A TV system is expected to last for 50000 hours before failure. Assume an exponential distribution...
A TV system is expected to last for 50000 hours before failure.
Assume an exponential distribution for the time until failure.
a) is the distribution skewed or symmetric?
b) what is the standard deviation of the length of time until
failure?
c) the system has been working continuously for the past 8500
hours and is still on. What is the expected time from now until
failure?
Data collected at an airport suggests that an exponential distribution with mean value 2.815 hours is...
Data collected at an airport suggests that an exponential
distribution with mean value 2.815 hours is a good model for
rainfall duration.
(a)
What is the probability that the duration of a particular
rainfall event at this location is at least 2 hours? At most 3
hours? Between 2 and 3 hours? (Round your answers to four decimal
places.)
at least 2 hoursat most 3 hoursbetween 2 and 3 hours
(b)
What is the probability that rainfall duration exceeds the...
Data collected at an airport suggests that an exponential distribution with mean value 2.815 hours is...
Data collected at an airport suggests that an exponential
distribution with mean value 2.815 hours is a good model for
rainfall duration.
(a)
What is the probability that the duration of a particular
rainfall event at this location is at least 2 hours?
At most 3 hours?
Between 2 and 3 hours?
(Round your answers to four decimal places.)
at least 2 hours
at most 3 hours
between 2 and 3 hours
(b)
What is the probability that rainfall duration...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Based on the loanable funds theory, explain how each of the following changes should impact interest...
- research paper: each student will be responsible for writing an argumentative research paper discussion a topic...
- In java based on the classes provided finish the program per the requirements: ----------------------------------------------Class1 package cardgame;...
- Identify two cultures and analyze the nurturing process within each culture and discuss the impact the...
- Digital security is an increasing concern is the Internet age. In order to protect sensitive information...
- the challenges experienced by companies considering full application of customer retention strategy in the face of...
- Respond to the following in a minimum of 175 words: The flow of a program is...
ADVERTISEMENT