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2 years ago

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Do male and female servers work the same number of hours? A sample of 25 female servers worked an average of 26 hours per week,

with a standard deviation of 2. A sample of 11 male servers worked an average of 23 hours per week, with a standard deviation of 4. Let μ 1 and μ 2 represent the typical number of hours worked by all female and male servers, respectively. Construct a 90% confidence interval for μ 1 − μ 2 , assuming normal populations with unequal variances.

1 answer:

Vera_Pavlovna [14]2 years ago

5 0

Answer:

Step-by-step explanation:

Given that

Group Group One Group Two

Mean 26.00 23.00

SD 2.00 4.00

SEM 0.40 1.21

N 25 11

where group I represents female servers and group II male servers.

We have to calculate confidence interval for 90% for difference in means

The mean of Group One minus Group Two equals 3.00

df = 34

standard error of difference = 0.993

t critical = 2.034 for 90% df 34

Hence confid. interval at 90%

=Mean diff ±2.034 * std error of diff

= (0.98, 5.02)

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In a New York Times/CBS News Poll, respondents were asked if it should be legal or illegal to send a text message while driving.

AnnZ [28]

Answer: $\dfrac2{201}$

Step-by-step explanation:

Number of persons said it is legal to text while driving = 8

Number of persons said it is illegal to text while driving = 804

Total persons sampled = 804+8 = 812

Since probability = $\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}$

The probability of randomly selecting someone who believes it should be legal to text while driving = $\dfrac{8}{804}=\dfrac2{201}$

Required probability = $\dfrac2{201}$

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2 years ago

In a sample of 53 walking canes, the average length was found to be 34.3in. with a variance of 1.9. Give a point estimate for th

Anna11 [10]

Answer:

1.38

Step-by-step explanation:

The point estimate for the population standard deviation of the length of the walking canes is given as the squareroot of variance. Since variance is provided as 1.9 then the standard deviation will be

$\sqrt 1.9=1.37840487520902\approx 1.38$

Therefore, rounded off to two decimal places, the standard deviation is approximately 1.38

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2 years ago

BD bisects m m Find m

amm1812

The text of the question is not visible in the answering window. I'll reproduce it here:

BD bisects <ABC.

m <ABD= 2.5x + 8.6

m<CBD = 3.5x - 3.4

Find m<ABC

Answer:

$m\angle ABC = 77.2^\circ$

Step-by-step explanation:

We have an angle ABC and a line BD bisecting it.

If an angle is bisected, then the two formed angles are congruent, that is

$m\angle ABD=m\angle CBD$

Substituting the algebraic expressions for both angles:

$2.5x + 8.6=3.5x - 3.4$

Subtracting 8.6 and 3.5x:

$2.5x - 3.5x = -8.6 - 3.4$

Operating:

$-x = -12$

$x = 12$

The two angles are:

$m\angle ABD=2.5x + 8.6=2.5(12) + 8.6=38.6^\circ$

$m\angle CBD=3.5x - 3.4 = 38.6^\circ$

As expected, both angles have the same measure.

The measure of the total angle ABC is twice any of those:

$m\angle ABC = 2*38.6^\circ=77.2^\circ$

$\mathbf{m\angle ABC = 77.2^\circ}$

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2 years ago

The distribution of lifetimes of a particular brand of car tires has a mean of 51,200 miles and a standard deviation of 8,200 mi

Orlov [11]

Answer:

a) 0.277 = 27.7% probability that a randomly selected tyre lasts between 55,000 and 65,000 miles.

b) 0.348 = 34.8% probability that a randomly selected tyre lasts less than 48,000 miles.

c) 0.892 = 89.2% probability that a randomly selected tyre lasts at least 41,000 miles.

d) 0.778 = 77.8% probability that a randomly selected tyre has a lifetime that is within 10,000 miles of the mean

Step-by-step explanation:

Problems of normally distributed distributions are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 51200, \sigma = 8200$

Probabilities:

A) Between 55,000 and 65,000 miles

This is the pvalue of Z when X = 65000 subtracted by the pvalue of Z when X = 55000. So

X = 65000

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{65000 - 51200}{8200}$

$Z = 1.68$

$Z = 1.68$ has a pvalue of 0.954

X = 55000

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{55000 - 51200}{8200}$

$Z = 0.46$

$Z = 0.46$ has a pvalue of 0.677

0.954 - 0.677 = 0.277

0.277 = 27.7% probability that a randomly selected tyre lasts between 55,000 and 65,000 miles.

B) Less than 48,000 miles

This is the pvalue of Z when X = 48000. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{48000 - 51200}{8200}$

$Z = -0.39$

$Z = -0.39$ has a pvalue of 0.348

0.348 = 34.8% probability that a randomly selected tyre lasts less than 48,000 miles.

C) At least 41,000 miles

This is 1 subtracted by the pvalue of Z when X = 41,000. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{41000 - 51200}{8200}$

$Z = -1.24$

$Z = -1.24$ has a pvalue of 0.108

1 - 0.108 = 0.892

0.892 = 89.2% probability that a randomly selected tyre lasts at least 41,000 miles.

D) A lifetime that is within 10,000 miles of the mean

This is the pvalue of Z when X = 51200 + 10000 = 61200 subtracted by the pvalue of Z when X = 51200 - 10000 = 412000. So

X = 61200

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{61200 - 51200}{8200}$

$Z = 1.22$

$Z = 1.22$ has a pvalue of 0.889

X = 41200

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{41200 - 51200}{8200}$

$Z = -1.22$

$Z = -1.22$ has a pvalue of 0.111

0.889 - 0.111 = 0.778

0.778 = 77.8% probability that a randomly selected tyre has a lifetime that is within 10,000 miles of the mean

4 0

2 years ago

Triangle DEF is congruent to TriangleGHJ by the SSS theorem. Which rigid transformation is required to map TriangleDEF onto Tria

inn [45]

Answer:

Rotation

Step-by-step explanation:

Given:

Triangle DEF is congruent to Triangle GHJ by the SSS theorem

To find: transformation required to map Triangle DEF onto Triangle GHJ

Solution:

Two figures are said to be congruent if they overlap each other.

Two polygons are said to be congruent if they have same size and shape.

A rotation is a transformation that turns a figure about the center of rotation.

Rotation transformation is required to map Triangle DEF onto Triangle GHJ

7 0

2 years ago

Read 2 more answers