If a − b ∈ P, then (a + c) − (b + c) = a − b is in P. Thus a + c

In a sample of 60 electric motors, the average efficiency (in percent) was 85 and the standard deviation was 2. Section 05.01 Ex

jasenka [17]

Answer:

95% confidence interval for the mean efficiency is [84.483 , 85.517].

Step-by-step explanation:

We are given that in a sample of 60 electric motors, the average efficiency (in percent) was 85 and the standard deviation was 2.

So, the pivotal quantity for 95% confidence interval for the population mean efficiency is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\mu$ = sample average efficiency = 85

$\sigma$ = sample standard deviation = 2

n = sample of motors = 60

$\mu$ = population mean efficiency

So, 95% confidence interval for the mean efficiency, $\mu$ is ;

P(-2.0009 < $t_5_9$ < 2.0009) = 0.95

P(-2.0009 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 2.0009 ) = 0.95

P( $-2.0009 \times {\frac{s}{\sqrt{n} }$ < ${\bar X - \mu}$ < $2.0009 \times {\frac{s}{\sqrt{n} }$ ) = 0.95

P( $\bar X -2.0009 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +2.0009 \times {\frac{s}{\sqrt{n} }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X -2.0009 \times {\frac{s}{\sqrt{n} }$ , $\bar X +2.0009 \times {\frac{s}{\sqrt{n} }$ ]

= [ $85 -2.0009 \times {\frac{2}{\sqrt{60} }$ , $85 +2.0009 \times {\frac{2}{\sqrt{60} }$ ]

= [84.483 , 85.517]

Therefore, 95% confidence interval for the population mean efficiency is [84.483 , 85.517].

8 0

3 years ago

those are currency exchange rates 1 us dollar = 7.76 hk dollars 1 us dollar =1.47 nk dollars work out the value of 1000 hk dolla

Alik [6]

Answer: 1000 HK dollars has the same value as 188.15 NZ dollars.

Step-by-step explanation:

We know that:

1 US dollar = 7.76 HK dollars

1 US dollar = 1.46 NZ dollars.

We have 1000 HK dollars, and we want to know the value in NZ dollars.

First, let's rewrite the 1000 HK dollars in US dollars.

Here we use the relation:

1 US dollar = 7.76 HK dollars

Then:

1 = (1 US dollar/7.76 HK dollars)

Then we can write:

1000 HK = (1000 HK)*1 = (1000 HK)*( (1 US /7.76 HK ))

1000 HK = (1000 HK/7.76 HK)* 1 US = 128.87 US

1000 HK = 128.87 US

Now we can use the relationship:

1 US = 1.46 NZ

Then:

1 = (1.46 NZ)/(1 US)

So we can rewrite:

128.87 US = (128.87 US)*1 = (128.87 US)*( (1.46 NZ)/(1 US))

128.87 US = (128.87 US/1 US)*1.46 NZ = 188.15 NZ

Then:

1000 HK = 128.87 US = 188.15 NZ

So we can conclude that 1000 HK dollars has the same value as 188.15 NZ dollars.

5 0

3 years ago

Korey completely covered a square counter top using 103.5 ft² of tile without any overlap. Which measurement is closest to the s

kaheart [24]

Answer:

d

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

If f(x) is a function and f(1) = 5, then which of the following could not be true?

Natasha_Volkova [10]

It can't be f(1) = 1 because a function can't have two images on the same x.

8 0

3 years ago

Read 2 more answers

Jeannie is an experienced business traveler, often traveling back and forth from San Francisco to the East Coast several times p

lesya692 [45]

Answer:

The probability that Jeannie will miss her flight because her total time for catching her plane exceeds one hour is 0.0026.

Jeannie should leave her office 55 minutes early.

Step-by-step explanation:

Let X = time it requires Jeannie to catch her plane.

The random variable X is normally distributed, $N(46, 5)$ .

Compute the probability that Jeannie will miss her flight because her total time for catching her plane exceeds one hour as follows:

$P(X>60)=P(\frac{X-\mu}{\sigma} >\frac{60-46}{5} )\\=P(Z>2.8)\\=1-P(Z$

The probability that Jeannie will miss her flight because her total time for catching her plane exceeds one hour is 0.0026.

Now, it is provided that Jeannie has 96% chance of catching her flight if she reaches under x minutes.

That is, P (X < x) = 0.96.

Compute the value of x as follows:

$P(X$

**Use the z-table to compute the value of z.

The value of z is 1.751.

Compute the value of x as follows:

$z=\frac{x-46}{5}\\ 1.751=\frac{x-46}{5}\\x=46+(1.751\times5)\\=54.755\\\approx 55$

Thus, Jeannie should leave her office 55 minutes early.

4 0

3 years ago

If a − b ∈ P, then (a + c) − (b + c) = a − b is in P. Thus a + c > b + c​

If a − b ∈ P, then (a + c) − (b + c) = a − b is in P. Thus a + c > b + c