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Diano4ka-milaya [45]
1 year ago
14

1 point

Mathematics
1 answer:
Elan Coil [88]1 year ago
7 0

Your current balance if you started the day with $100 in your account is $73

First step is to calculate the total cash at bank

Using this formula

Total Cash at bank= Cash at bank + Deposit

Let plug in the formula

Total Cash at bank=$100+90

Total Cash at bank=$190

Second step is to calculate the amount debited

Debit amount=($60+$3)+($34+$20)

Debit amount=$63+$54

Debit amount=$117

Now let determine your current balance

Current balance=Total cash at bank-Amount debited

Let plug in the formula

Current balance=$190-117

Current balance=$73

Your current balance if you started the day with $100 in your account is $73

Learn more here:

brainly.com/question/22165984

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An article suggested that yield strength (ksi) for A36 grade steel is normally distributed with μ = 42 and σ = 5.5.
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Answer:

a)P( X

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P(X   (b)

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But we know which value of z satisfy the previous equation so then we can do this:

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Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

X \sim N(42,25.5)  

Where \mu=42 and \sigma=5.5

And we want this probability:

P( X

And using the z score formula given by:

z = \frac{x -\mu}{\sigma}

We got:

P( X

We want this probability:

P( X >64)

And using the z score formula given by:

z = \frac{x -\mu}{\sigma}

We got:

P( X >64) =P(Z> \frac{64-42}{5.5}) =P(Z>4)=0.0000316

Part b

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.674

And if we solve for a we got

a=42 +0.674*5.5=45.707

So the value of height that separates the bottom 75% of data from the top 25% is 45.707.  

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