Question

Exercise 2:

The lifetime of a battery follows a normal distribution with mean μ = 3 years and σ = 0.5 years.

1. What is the probability that the battery lasts more than 2.3
years?

2. What is the probability that the lifetime of the battery is
between 2 and 4.3years?

3. Find the value of x above which lies the 12% most lasting
batteries.

Answer #1

The lifetime of a certain battery follows a normal distribution
with a mean 276 minutes and standard deviation 25 minutes. We took
a random sample of 100 of these batteries. What is the probability
that the sample mean of the lifetime will be less than 270
minutes?

The lifetime of a certain battery follows a normal distribution
with a mean 276 minutes and standard deviation 20 minutes. We took
a random sample of 100 of these batteries. What is the probability
that the sample mean of the lifetime will be less than 270
minutes?
A.0.9987
B.0.0013
C.0.4987
D.0.3821

Suppose the longevity of iPad batteries can be modeled by a
normal distribution with mean μ = 8.2 hours and standard deviation
σ = 1.2 hours.
a. Find the probability a randomly selected iPad lasts less than
10 hours.
b. Find the 25th percentile of the battery times.

The lifetime of a part follows a gamma distribution with a mean
lifetime of 2 years and a variance of 5 years squared. what is the
probability that a random part dies within the first 3 years?

The type of battery in Jim's laptop has a lifetime (in years)
which follows a Weibull distribution with parameters α = 2 and β =
4 . The type of battery in Jim's tablet has a lifetime (in years)
which follows an exponential distribution with parameter λ = 1 / 4
. Find the probability that the lifetime of his laptop battery is
less than 2.2 years and that the lifetime of his tablet battery is
less than 3.1 years.

Energetic Co., a battery manufacturer, claims their battery
lasts for 67.22 months with a standard deviation of 5.863 months.
You randomly sample 35 of these batteries. Assuming the
distribution for the battery lifetime is approximately normal, what
is the probability the average lifetime is less than 66.14?
Question 8 options:
1)
0.5731
2)
0.8621
3)
0.4269
4)
0.1379
5)
0.2223

An electric scooter manufacturer uses batteries that follow a
normal distribution with a mean lifetime of 3 years and a standard
deviation of 3 months. Is the manufacturer safe in providing a
4-year warranty on the batteries?

The battery life of a certain fire alarm, denoted by X, follows
an exponential distribution with mean 3 hours. Suppose we take a
random sample of 36 fire alarms. Answer the following
questions.
A. Find the probability that a single fire alarm will operate
for at least 6 hours.
B. Find the probability that the total battery lifetime based on
the 36 fire alarms will be more than 126 hours.
C.
If the sample mean was 3.5, find a 95%...

Battery life follows a normal continuous probability
distribution with a population mean = 300 hours and a population
standard deviation of 30 hours.
a. What is probability that a battery tested will last for less
than 270 hours?
b. What is probability that a battery tested will last between
270 and 330 hours?

battery life follows a normal continuous probability
distribution with a population mean = 300 hours and a population
standard deviation of 30 hours. What is probability that a battery
tested will last for less than 270 hours?
What is probability that a battery tested will last between 270
and 330 hours?
The weakest 10% of the population will not exceed what battery
life?

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