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Tema [17]
3 years ago
11

The lifespan of a 60-watt lightbulb produced by a company is normally distributed with a mean of 1450 hours and a standard devia

tion of 8.5 hours. if a 60-watt light bulb produced by this company is selected at random, what is the probability that its lifespan will be between 1440 and 1465 hours
Mathematics
1 answer:
Flura [38]3 years ago
8 0
To evaluate the probability that the lifespan will be between 1440 and 1465 hours will be given by:
P(1440<x<1465)
using the z-score formula we obtain:
z=(x-μ)/σ
where:
μ=1450
σ=8.5
hence
when x=1440
z=(1440-1450)/8.5
z=-1.18
P(z<-1.18)=0.1190

when x=1465
z=(1465-1450)/8.5
z=1.77
P(z<1.77)=0.9625

hence:
P(1440<x<1465)
=0.9625-0.1180
=0.8445
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Answer:

.b. It is one‐half as large as when n = 100.

Step-by-step explanation:

Given that a  simple random sample of 100 batteries is selected from a process that produces batteries with a mean lifetime of 32 hours and a standard deviation of 3 hours.

i.e. s = 0.3

we obtain se of sample by dividing std devitation by the square root of sample size

i.e. s= \frac{3}{\sqrt{n} }

when n =100 this = 0.3 and

when n =400 this equals 0.15

We find that when sample size is four times as large as original, std deviation becomes 1/2 of the original

Correction option is

.b. It is one‐half as large as when n = 100.

7 0
3 years ago
Select the correct solution set.<br> X+17 5 -3<br> {XIX2-20)<br> {XIXS-20)<br> [xl xs 14
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Answer:

x≤-20

Step-by-step explanation:

x+ 17≤-3

Subtract 17 from each side

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3 0
4 years ago
Lena found a 5/8
DENIUS [597]

Answer:

Naomi had the correct measurement the ring weighed 0.625 carats

Step-by-step explanation:

* The diamond ring weighed 5/8 carats

- To know who is right lets change the fraction 5/8 to a decimal number

∵ 5/8 means 5 ÷ 8

- 5 is smaller than 8 so we will multiply it by 10 and

 insert decimal point in the quotient (answer of division)

∴ It will be 50 ÷ 8 = 6 and remainder 2/8 ⇒ 1/4

∴ The quotient = 0.6 and remainder 1/4

- 1 is smaller than 4 so we will multiply it by 10

∴ It will be 10 ÷ 4 = 2 and remainder 2/4 ⇒ 1/2

∴ The quotient = 0.62 and remainder 1/2

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∴ It will be 10 ÷ 2 = 5 without remainder

∴ The quotient = 0.625

* Naomi had the correct measurement the ring weighed 0.625 carats

8 0
3 years ago
Read 2 more answers
The area of a playground is 336 yd2. The width of the playground is 5 yd longer than its length. Find the length and width of th
kondaur [170]
L=16
W=21

Set up a systems of equations: 
x=length 
y=width 

xy=336
x+5=y

Use substitution to solve: 
x(x+5)=336
x^2+5x=336 

Solve using factoring: 
x^2+5x-336=0
(x-16)(x+21)=0
x=16 and x= -21 
Since length can't be negative, l=16 

To find width, plug length into the first equation: 
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y=21 

So...
L=16
<span>W=21</span>
7 0
3 years ago
Read 2 more answers
Janet deposited $9,600 into an account that pays 4.4 interest, compounded daily. At the end of nine months, how much interest ha
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bearing in mind that 9 months is not even a year, but since there are 12 months in a year, then 9 months is really 9/12 years.


\bf ~~~~~~ \stackrel{\textit{daily}}{\textit{Continuously}} \textit{Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$9600\\ r=rate\to 4.4\%\to \frac{4.4}{100}\dotfill &0.044\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases} \\\\\\ A=9600e^{0.044\cdot \frac{3}{4}}\implies A=9600e^{0.033}\implies A\approx 9922.09 \\\\\\


\bf \stackrel{\textit{interest earned}}{9922.09-9600\implies 322.09}

5 0
3 years ago
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