Mathematics, 18.03.2020 18:21, albattatasraap5wymy

The life span of a battery is the amount of time the battery will last. The distribution of life span for a certain type of battery is approximately normal with mean 2.5 hours and standard deviation 0.25 hour. Suppose one battery will be selected at random. Which of the following is closest to the probability that the selected battery will have a life span of at most 2.1 hours?

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answered: Brandikitts

The probability that the selected battery will have a life span of at most 2.1 hours is 0.0548.

Given information:

The life span of a battery is the amount of time the battery will last.

The distribution of life span for a certain type of battery is approximately normal with a mean of 2.5 hours and a standard deviation of 0.25 hours.

The z-value for the probability that the selected battery will have a life span of at most 2.1 hours will be calculated as,

$z=\dfrac{x-\mu}{\sigma}\\z=\dfrac{2.1-2.5}{0.25}\\z=-1.6$

Now, use the standard normal distribution table or curve to get the value of required probability as,

P(x=2.1)=0.0548

Therefore, the probability that the selected battery will have a life span of at most 2.1 hours is 0.0548.

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answered: annalaurie7

0.0548

Step-by-step explanation:

The distribution of life span for a certain type of battery is approximately normal with mean 2.5 hours and standard deviation 0.25 hour.

To find the the probability that a selected battery will have a life span of at most 2.1 hours, we need to first determine the z-score for x=2.1 hours using

$z = \frac{x - \mu}{ \sigma}$

We substitute the values to get:

$z = \frac{2.1 - 2.5}{0.25} = - 1.6$

We read read -1.6 from the standard normal distribution table to get:

P(X≤2.1)=0.0548

answered: Guest

e^-kt = n/n0 = 0.79

-kt = ln 0.79

t = - ln 0.79/0.0001

= 2357 years

step-by-step explanation:

answered: Guest

a. geometricb. g[h] = (3/4)·g[h-1]; g[1] = 384c. g[h] = 384·(3/4)^(h-1)d. g[12] ≈ 16.2183 gallonse. g[12] ≈ 64.8732 quarts

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt