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2 years ago

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The number of days (X) after mailout it takes a utility company to receive payment for a customer’s bill is a normal random vari

able with a mean of 31 days and a standard deviation of 6 days.The latest 2.5% of bills will be received more than how many days after mailout?

1 answer:

Monica [59]2 years ago

4 0

Answer:

The latest 2.5% of bills will be received in 20 more days after mail-out.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 31 days

Standard Deviation, σ = 6 days

We are given that the distribution of The number of days (X) is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

$P(X \leq x) = 0.025$

We have to find the value of x such that the probability is 0.025

$P(X \leq x) = 0.025$

$P( X \leq x) = P( z \leq \displaystyle\frac{x - 31}{6})=0.025$

Calculation the value from standard normal z table, we have,

$P( z \leq -1.960) = 0.025$

$\displaystyle\frac{x - 31}{6} = -1.960\\x = 19.24 \approx 20$

Hence, the latest 2.5% of bills will be received in 20 more days after mail-out.

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The quality control manager at a light bulb factory needs to estimate the mean life of a batch (population) of light bulbs. We a

Nadusha1986 [10]

Answer:

<em>a)95% confidence intervals for the population mean of light bulbs in this batch</em>

(325.5 ,374.5)

b)

<em>The calculated value Z = 4 > 1.96 at 0.05 level of significance</em>

<em>Null hypothesis is rejected </em>

<em>The manufacturer has not right to take the average life of the light bulbs is 400 hours.</em>

Step-by-step explanation:

Given sample size n = 64

Given mean of the sample x⁻ = 350

Standard deviation of the Population σ = 100 hours

The tabulated value Z₀.₉₅ = 1.96

<em>95% confidence intervals for the population mean of light bulbs in this batch</em>

<em></em> $(x^{-} - Z_{\frac{\alpha }{2} } \frac{S.D}{\sqrt{n} } , x^{-} + Z_{\frac{\alpha }{2} }\frac{S.D}{\sqrt{n} } )$ <em></em>

<em></em> $(350 - 1.96\frac{100}{\sqrt{64} } , 350 + 1.96\frac{100}{\sqrt{64} } )$ <em></em>

$(350 -24.5, 350 +24.5)$

(325.5 ,374.5)

b)

<u><em>Explanation</em></u>:-

Given mean of the Population μ = 400

Given sample size n = 64

Given mean of the sample x⁻ = 350

Standard deviation of the Population σ = 100 hours

<u><em>Null hypothesis</em></u> : H₀:The manufacturer has right to take the average life of the light bulbs is 400 hours.

μ = 400

<u><em>Alternative Hypothesis: H₁:</em></u> μ ≠400

<u><em>The test statistic </em></u>

$Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }$

$Z = \frac{350 -400}{\frac{100}{\sqrt{64} } }$

|Z| = |-4|

The tabulated value Z₀.₉₅ = 1.96

The calculated value Z = 4 > 1.96 at 0.05 level of significance

Null hypothesis is rejected.

<u><em>Conclusion:</em></u>-

The manufacturer has not right to take the average life of the light bulbs is 400 hours.

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jeka57 [31]

Answer: square root 50 that does not belong

Step-by-step explanation:

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2 years ago

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solution:

The probability mass function for binomial distribution is,

Where,

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Consider x to be the number of non-conformities. It follows a binomial distribution with n being 50 and p being 0.03. That is,

binomial (50,0.02)

Also, the estimate of the true probability is,

p∧ = x/50

The probability mass function for binomial distribution is,

Where,

X=0,1,2,3,…..; q=1-p

The calculation is obtained as

P(p^ ≤ 0.06) = p(x/20 ≤ 0.06)

= 50cx ₓ (0.03)x ₓ (1-0.03)50-x

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=( ₓ (0.03)0 ₓ (1-0.03)50-0 + ₓ (0.03)1 ₓ (1-0.03)50-1 + ₓ (0.03)2 ₓ (1-0.03)50-2 ₓ (0.03)3 ₓ (1-0.03)50-3 )

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Option B: $\frac{1}{(m-4)(m-3)}$ is the correct answer.

Explanation:

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Simplifying the expression, we have,

$\frac{m+3}{m^{2}-16}\times\frac{m+4}{m^2-9}$

Factor the equations, $m^{2}-16\right$ and $m^{2}-9$ ,we get,

$m^{2}-16\right=m^{2}-4^{2}=(m+4)(m-4)$

$m^{2}-9=m^{2}-3^2=(m+3)(m-3)$

Substituting these factored expressions in the above expression, we have,

$\frac{m+3}{(m+4)(m-4)}\times\frac{m+4}{(m+3)(m-3)}$

Cancelling the common terms $m+3$ and $m+4$ , we get,

$\frac{1}{(m-4)(m-3)}$

Thus, the expression equivalent to $\frac{(\frac{m+3}{m^2-16}) }{(\frac{m^2-9}{m+4} )}$ is $\frac{1}{(m-4)(m-3)}$

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