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lapo4ka [179]
2 years ago
13

The time at which the mailman delivers the mail to ace bike shop follows a normal distribution with mean 2:00 pm and standard de

viation of 15 minutes.
Mathematics
1 answer:
ivolga24 [154]2 years ago
4 0

There are three questions related to this problem.


First, the probability of the mail will arrive after 2:30 PM


<span>Find the z-score of 2:30 which is 30 minutes after 2:00.</span>

<span>
z(2:30) = (2:30 – 2:00)/15 = -30/15 = -2</span>

<span>
P(x < 2:30) = P(z<-2) = 0.0228</span>

<span>
</span>

Second, the probability of the mail will arrive at 1:36 PM

<span>Find the z-score of 1:36 which is 24 minutes before 2:00.</span>

<span>
z(1:36) = (1:36 – 2:00)/15 = -24/15 = -1.6</span>

<span>
P(x < 1:36) = P(z<-1.6) = 0.0548</span>

 

Lastly, the probability of the mail will arrive between 1:48 PM and 2:09 PM


Find the z-score of 1:46 and 2:09 PM which will result to a z value of 0.034599


<span>P(1:48 < x < 2:09) = P(z<0.034599) = 0.5138</span>

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Answer:

27 hours

Step-by-step explanation:

The regular hours are paid normally, 21/hr hence working for 40 hours, Michael earns 40*21=$840

To work x hours paid overtime as 1.5 of the normal rate, the rate would be $21*1.5=$31.5/hr

X hours multiplied by rate of $31.5/hr should be at least equal to $840

31.5x>=840

X>=840/31.5>=26.6667 hours and when rounded off

X is 27 hours

6 0
2 years ago
Which equation represents the line shown on the graph?
Mama L [17]

Hello there,

To find out the equation you use the slope intercept form...

y = mx + b

M is the slope and b is where the line crosses the y-axis...

Now to find the slope you count the distance from two points so...

The distance from (0,2) to (1,5) is 3 units up and 1 unit over.

So the correct answer should be...

y = 3x + 2


Answer: w = 3z + 2


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2 years ago
Explain why there are two sine ratios, two cosine ratios, and two tangent ratios for any right triangle
taurus [48]
Each angle has a sin, cos, and tan associated with it.
in a right angled triangle there are two other angles which each have ratios.
5 0
1 year ago
Read 2 more answers
Chicken eggs can be categorized as large if they weigh at least 2 ounces. Clare weighs 48 large eggs and finds that they have a
weqwewe [10]

Answer:

0.08 ounces is interpreted as the Mean Absolute Deviation and this means that

the various weights of each of the 48 eggs deviates from the mean of the egg (2.1 ounces)by 0.08 ounces.

Step-by-step explanation:

Mean Absolute Deviation of a data set is defined as the distance or the deviation between a given data set and the calculated mean.

Mean Absolute Deviation tells us about how much a data set varies from it's mean.

From the above question, we are told that after weighing 48 eggs we have a mean of 2.1 ounces and mean deviation of 0.08 ounces

Therefore this means that the various weights of each of the 48 eggs deviates from the mean of the egg (2.1 ounces)by 0.08 ounces

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2 years ago
Suppose the weights of fish caught from pier 1 and pier 2 are normally distributed with equal population standard deviations. Th
madreJ [45]

Answer:

<em>H₀</em>: <em>μ</em>₁ = <em>μ</em>₂ vs, <em>Hₐ</em>: <em>μ</em>₁ > <em>μ</em>₂.

Step-by-step explanation:

A two-sample <em>z</em>-test can be performed to determine whether the claim made by the owner of pier 1 is correct or not.

It is provided that the weights of fish caught from pier 1 and pier 2 are normally distributed with equal population standard deviations.

The hypothesis to test whether the average weights of the fish in pier 1 is more than pier 2 is as follows:

<em>H₀</em>: The weights of fish in pier 1 is same as the weights of fish in pier 2, i.e. <em>μ</em>₁ = <em>μ</em>₂.

<em>Hₐ</em>: The weights of fish in pier 1 is greater than the weights of fish in pier 2, i.e. <em>μ</em>₁ > <em>μ</em>₂.

The significance level of the test is:

<em>α</em> = 0.05.

The test is defined as:

z=\frac{(\bar x_{1}-\bar x_{2})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}}

The decision rule for the test is:

If the <em>p</em>-value of the test is less than the significance level of 0.05 then the null hypothesis will be rejected and vice-versa.

6 0
2 years ago
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