A study conducted at a certain college shows that 54% of the school's graduates move to a different state after graduating. Find the probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

Answers

Answer 1

Answer:

Answer:

99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

Step-by-step explanation:

For each graduate, there are only two possible outcomes. Either they move to a different state, or they do not. The probability of a graduate moving to a different state is independent of other graduates. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

In which $C_(n,x)$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_(n,x) = (n!)/(x!(n-x)!)$

And p is the probability of X happening.

54% of the school's graduates move to a different state after graduating.

This means that $p = 0.54$

7 randomly selected graduates

This means that $n = 7$

Find the probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

Either none moves, or at least one does. The sum of the probabilities of these events is 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$ . Then

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

$P(X = 0) = C_(7,0).(0.54)^(0).(0.46)^(7) = 0.0044$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0044 = 0.9956$

99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

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Lucio is buying candy. He buys 1.5 pounds of gummy bears which cost $1.88 per pound and 0.8 pounds of caramels which cost $2.75 per pound. What is the total cost of the candy?

Answers

Answer:

$5.02

Step-by-step explanation:

Answer:

5.02

Step-by-step explanation:

According to a medical journal, the average daily U.S. diet contains 6,000 mg of sodium. How many grams is this?

Answers

OK so for every gram it is 1,000 mg so the answer to your question will be for 6,000 mg it will be 6 grams.

You want to create an 80% confidence interval for the average age of people who attend U of O football games. You take a sample of 100 attendees and find the average age to be 43.7 years old with a standard deviation of 7 years. Find the value of t* for this confidence interval. Do not round your answer. Write your answer in decimal form, not as a fraction or percent.

Answers

Answer:

80% confidence interval for the average age of people who attend U of O football games is [42.795 , 44.604].

Step-by-step explanation:

We are given that a sample of 100 attendees and find the average age to be 43.7 years old with a standard deviation of 7 years.

So, the pivotal quantity for 80% confidence interval for the population average start up cost is given by;

P.Q. = $(\bar X - \mu)/((s)/(√(n) ) )$ ~ $t_n_-_1$

where, $\mu$ = sample average age = 43.7 years old

$\sigma$ = sample standard deviation = 7 years

n = sample of attendees = 100

$\mu$ = population average age of people

So, 80% confidence interval for the average age of people, $\mu$ is ;

P(-1.2915 < $t_9_9$ < 1.2915) = 0.80

P(-1.2915 < $(\bar X - \mu)/((s)/(√(n) ) )$ < 1.2915) = 0.80

P( $-1.2915 * {(s)/(√(n) )$ < ${\bar X - \mu}$ < $1.2915 * {(s)/(√(n) )$ ) = 0.80

P( $\bar X -1.2915 * {(s)/(√(n) )$ < $\mu$ < $\bar X +1.2915 * {(s)/(√(n) )$ ) = 0.80

80% confidence interval for $\mu$ = [ $\bar X -1.2915 * {(s)/(√(n) )$ , $\bar X +1.2915 * {(s)/(√(n) )$ ]

= [ $43.7 -1.2915 * {(7)/(√(100) )$ , $43.7 +1.2915 * {(7)/(√(100) )$ ]

= [42.795 , 44.604]

Therefore, 80% confidence interval for the population average age of people who attend U of O football games is [42.795 , 44.604].

1. number 5 added to three times the product of M and N.2. product of number Y and Z subtracted from 10.
3. sum of number X and Y subtracted from their products.
4. workings pls

Answers

Answer:

a) 5 - mn

Step-by-step explanation: its correct

2 ( x - 6 ) = 3 ( x + 9 )

Answers

Steps to solve:

2(x - 6) = 3(x + 9)

~Distribute both sides

2x - 12 = 3x + 27

~Add 12 to both sides

2x = 3x + 39

~Subtract 3x to both sides

-x = 39

~Divide both sides by -1

x = -39

Best of Luck!

Answer:

2×-12=3×+27

2×-3×=27+12

-×=39

Step-by-step explanation:

Grouping like terms

then simplify to get x

Solve the system by elimination:
36x-63y=7
-24x+42y=0

Answers

Answer:sorry I don't think itis possible with elimination method if it is possible you can post it in the comment section

Step-by-step explanation:

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