One hundred students were surveyed about whether they recycle regularly. The results are shown in

Given that the chord ef is a diameter of circle d which of the following names major arc

zubka84 [21]

1) Diameter = Line MN, Chord = Line LN
<span>2) B --- GFC </span>
<span>3) C --- GCE </span>

4 0

3 years ago

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

2 years ago

Sheila needs to hire a baby sitter for the evening.

marissa [1.9K]

Answer: The answer is 21

5 0

2 years ago

In a city, the distance between the library and the police station is 3 miles less than twice the distance between the police st

deff fn [24]

The distance between the police station and the fire station is x.
The distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station, so it is 2x-3. This distance is equal to 5 miles.

$2x-3=5 \\
2x=5+3 \\
2x=8 \\
x=\frac{8}{2} \\
x=4$

The police station and the fire station are 4 miles aparat.

5 0

2 years ago

Read 2 more answers

The shortest side of a right triangle measures 11m. The lengths of the other two sides are consecutive integers. Find the length

uranmaximum [27]

Interesting question. Let the 2 unknown sides be x and x+1.
Then (11 m)^2 + x^2 = sum of the squares of the 2 shortest sides
= (x+1)^2

121 + x^2 = x^2 + 2x + 1. Then 121 = 2x + 1, and 2x = 120, or x = 60.

Then the hyp. has length 60+1= 61.

We must check these results. Using the Pyth. Thm. (a^2 + b^2 = c^2),

11^2 + 60^2 = 61^2
121 + 3600 = 3721 This is true, so our answers are correct.

The longer side is 60 and the hyp. has length 61.

4 0

3 years ago