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Artist 52 [7]
3 years ago
15

5. A waiter earns $128 for 6 hours of work. The total included $86 in tips.

Mathematics
1 answer:
vovikov84 [41]3 years ago
3 0

Answer:

$7 per hour

Step-by-step explanation:

$128 minus the $86 in tips leaves $42

42 divided by 6 is 7 so the waiter earns $7

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A sample size 25 is picked up at random from a population which is normally
Margarita [4]

Answer:

a) P(X < 99) = 0.2033.

b) P(98 < X < 100) = 0.4525

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 100 and variance of 36.

This means that \mu = 100, \sigma = \sqrt{36} = 6

Sample of 25:

This means that n = 25, s = \frac{6}{\sqrt{25}} = 1.2

(a) P(X<99)

This is the pvalue of Z when X = 99. So

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{99 - 100}{1.2}

Z = -0.83

Z = -0.83 has a pvalue of 0.2033. So

P(X < 99) = 0.2033.

b) P(98 < X < 100)

This is the pvalue of Z when X = 100 subtracted by the pvalue of Z when X = 98. So

X = 100

Z = \frac{X - \mu}{s}

Z = \frac{100 - 100}{1.2}

Z = 0

Z = 0 has a pvalue of 0.5

X = 98

Z = \frac{X - \mu}{s}

Z = \frac{98 - 100}{1.2}

Z = -1.67

Z = -1.67 has a pvalue of 0.0475

0.5 - 0.0475 = 0.4525

So

P(98 < X < 100) = 0.4525

6 0
3 years ago
Write 9.68 x 104 in standard form?
-Dominant- [34]

Answer:

1006.72

Step-by-step explanation:

Multiply 9.68 by 104

7 0
3 years ago
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Before you make an offer on a home, you should first make sure your mortgage loan application has received a
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6 0
3 years ago
Can someone help me with this first one to answer gets brainllest and 20 points.
Afina-wow [57]

Answer:

Sorry i don't get this at all. what grade is this ?!!?!?!?

Step-by-step explanation:

5 0
3 years ago
Nattalie picked 135 berries in 15 minutes at this rate how long will it take her to pick 486 berries
forsale [732]
Well, If she takes 15 minutes to pick 135 berries, 30 minutes total would be 270 berries, so if you take another 15 minutes picking berries it would be a total of 405 berries but you still need 81 more. so if she can pick 405 in 45 minutes, it would be around a hour and something. 

Hope I helped or at least made you think about it

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3 years ago
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