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bekas [8.4K]
3 years ago
5

The lifetime of a battery in a certain application is normally distributed with mean μ = 16 hours and standard deviation σ = 2 h

ours. What is the probability that a battery will last more than 19 hours?
Mathematics
1 answer:
DaniilM [7]3 years ago
5 0

Answer:

Probability that a battery will last more than 19 hours is 0.0668.

Step-by-step explanation:

We are given that the lifetime of a battery in a certain application is normally distributed with mean μ = 16 hours and standard deviation σ = 2 hours.

<em>Let X = lifetime of a battery in a certain application</em>

So, X ~ N(\mu=16,\sigma^{2} =2^{2})

The z-score probability distribution for normal distribution is given by;

               Z = \frac{  X -\mu}{\sigma}  ~ N(0,1)

where, \mu = mean lifetime = 16 hours

            \sigma = standard deviation = 2 hours

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, the probability that a battery will last more than 19 hours is given by = P(X > 19 hours)

  P(X > 19) = P( \frac{  X -\mu}{\sigma} > \frac{19-16}{2} ) = P(Z > 1.50) = 1 - P(Z \leq 1.50)

                                              = 1 - 0.9332 = 0.0668

<em>Now, in the z table the P(Z </em>\leq<em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.</em>

Hence, the probability that a battery will last more than 19 hours is 0.0668.

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Answer: The common ratio is -2

-----------------------------------

Explanation: 

To get the common ratio r, we divide any term by the previous one

One example:
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Another example:
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Side Note: each term is multiplied by -2 to get the next term

============================================================
Part B

Answer:
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-----------------------------------

Explanation:

Recall that any geometric sequence has the nth term
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where the 'a' on the right side is the first term and r is the common ratio

The first term given to use is a = 1 and the common ratio found in part A above was r = -2
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============================================================
Part C

Answer: The next three terms are 16, -32, 64

-----------------------------------

Explanation:

We can simply multiply each previous term by -2 to get the next term. Do this three times to generate the next three terms

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Then plug in n = 6
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a(6) = (-2)^(5)
a(6) = -32 .... which matches with what we got earlier

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a(n) = (-2)^(n-1)
a(7) = (-2)^(7-1)
a(7) = (-2)^(6)
a(7) = 64 .... which matches with what we got earlier

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