What x^2 x 3x + 1000x please help

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and

Firdavs [7]

Answer:

1a

$P(39 < X < 48 ) = 0.8767$

1b

95% of all sample means will fall between $40.1 < \mu < 49.9$

1c

$\= x = 41. 795$

2

$n = 25$

Step-by-step explanation:

From the question we are told that

The mean is $n = 45$

The population standard deviation is $\sigma = 10$

The sample size is n = 16

Generally the standard error of the mean is mathematically represented as

$\sigma_{x} = \frac{ \sigma}{\sqrt{n} }$

=> $\sigma_{x} = \frac{ 10 }{\sqrt{16 } }$

=> $\sigma_{x} = 2.5$

Generally the probability that the sample mean will be between 39 and 48 minutes is

$P(39 < X < 48 ) = P( \frac{ 39 - 45}{ 2.5} < \frac{X - \mu }{\sigma } < \frac{ 48 - 45}{ 2.5} )$

=> $P(39 < X < 48 ) = P(-2.4 < Z< 1.2 )$

=> $P(39 < X < 48 ) = P( Z< 1.2 ) - P(Z < -2.4)$

From the z table the area under the normal curve to the left corresponding to 1.2 and -2.4 is

=> $P( Z< 1.2 ) = 0.88493$

and

$P( Z< - 2.4 ) = 0.0081975$

So

$P(39 < X < 48 ) = 0.88493 -0.0081975$

=> $P(39 < X < 48 ) = 0.8767$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E = 1.96 * 2.5$

=> $E =4.9$

Generally the 95% of all sample means will fall between

$\mu -E < and \mu +E$

=> $45 -4.9\ and \ 45 + 4.9$

Generally the value which 90% of sample means is greater than is mathematically represented

$P( \= X > \= x ) = 0.90$

=> $P( \= X > \= x ) = P( \frac{\= X - \mu }{ \sigma_x} > \frac{\= x -45 }{ 2.5} ) = 0.90$

=> $P( \= X > \= x ) = P( Z > z ) = 0.90$

Generally from the z-table the critical value of 0.90 is

$z = -1.282$

$\frac{\= x -45 }{ 2.5} = -1.282$

=> $\= x = 41. 795$

Considering question 2

Generally we are told that the standard deviation of the mean to be one fifth of the population standard deviation, this is mathematically represented as

$s = \frac{1}{5} \sigma$

Generally the standard deviation of the sample mean is mathematically represented as

$s = \frac{\sigma }{ \sqrt{n} }$

=> $\frac{1}{5} \sigma = \frac{\sigma }{ \sqrt{n} }$

=> $n = 5^2$

=> $n = 25$

5 0

3 years ago

What fraction would you add to 29/6 to make 4

Zigmanuir [339]

Keeping in mind that 29/6 is greater than 4, is actually 4 and 5/6, so the amount we'll "add" will be a negative one.

$\bf \cfrac{29}{6}+x=4\implies x=4-\cfrac{29}{6}\implies x=\cfrac{4}{1}-\cfrac{29}{6}\implies x=\cfrac{(6)4-(1)29}{6}
\\\\\\
x=\cfrac{24-29}{6}\implies x=\cfrac{-5}{6}\\\\
-------------------------------\\\\
\cfrac{29}{6}+\left( -\cfrac{5}{6} \right)=4$

8 0

3 years ago

Suppose Charli D'Amelio posted 40 dance videos to TikTok. If 65% of the videos have her making up her own moves, how many of the

dolphi86 [110]

Answer:

14 dance videos

Step-by-step explanation:

4 0

3 years ago

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31. You work 35 hours/week for 52 weeks and are given the option to be paid hourly or to go on salary. In which situation will y

ivann1987 [24]

Answer:

Option B

Step-by-step explanation:

<u>Calculate and compare:</u>

A) $32000
B) $18.5*35*52 = $33670
C) $30000 + 5% = $30000 + $1500 = $31500
D) $17.5*35*52 + $1500 = $33350

7 0

2 years ago

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It took Shawn 6 hours to walk to Susan's house at 2 kilometers per hour. How far is it between Shawn's house and Susan's house?

rodikova [14]

Answer:

12km

Step-by-step explanation:

this really is actually kind of simple so it takes shawn 6 hours to get there at a speed of 2 kilometer per hour so you take the time and you X it by the speed therefor 6 X 2 = 12 and that would be your answer

7 0

3 years ago

Read 2 more answers