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Tju [1.3M]
3 years ago
14

The average credit card debt for college seniors is $22,199 with a standard deviation of $5300. What is the probability that a s

ample of 30 seniors owes a mean of more than $20,200? Round answer to 4 decimal places. Answer:
Mathematics
1 answer:
noname [10]3 years ago
3 0

Answer:

Step-by-step explanation:

The number of samples is large(greater than or equal to 30). According to the central limit theorem, as the sample size increases, the distribution tends towards normal. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 22199

σ = 5300

n = 30

the probability that a senior owes a mean of more than $20,200 is expressed as

P(x > 20200)

Where x is a random variable representing the average credit card debt for college seniors.

For n = 30,

z = (20200 - 22199)/(5300/√30) =

- 2.07

Looking at the normal distribution table, the probability corresponding to the z score is 0.0197

P(x > 20200) = 0.0197

You might be interested in
What is the smallest prime number p such that
Ne4ueva [31]

The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.

<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>

The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.

i.e.

  • p^3 + 4p^2 + 4p

By factorization, we have:

  • = p(p+2)²

Now, to get exactly 30 divisor.

  • (p+2)² requires to give us 15 factors.

Therefore, we can have an equation p + 2 = p₁ × p₂²

where:

  • p₁ and  p₂ relate to different values of odd prime numbers.

So, for the least values of p + 2, Let us assume that:

  • p₁ = 5 and p₂ = 3

p + 2 = 5 × 3²

p + 2 = 5 × 9

p + 2 = 45

p = 45 - 2

p = 43

Therefore, we can conclude that the smallest prime number p such that

p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.

Learn more about prime numbers here:

brainly.com/question/145452

#SPJ1

8 0
1 year ago
Aaron needs a total of $410 to buy a new bicycle. He has $35 saved. He earns $15 each week delivering newspapers. How many weeks
Ostrovityanka [42]
35+15x=410
410-35=375
375/15=25
He will need to work 25 weeks.
3 0
3 years ago
Help me wiht this plssss
yulyashka [42]

Answer:

well you find. out how many all of them measure. and add them and then that answer multiply of the main number

Step-by-step explanation:

first add up all of the lengths and then find that answer multiply it to the main number and then you will get your anwer it's a 2 step problem

7 0
2 years ago
A researcher is going to estimate the average typing speed of students of a college. He selects a random sample of 20 students a
Stella [2.4K]

Answer:

The margin of error of the 90% confidence interval of a student's average typing speed is of 1.933 wpm.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 20 - 1 = 19

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 19 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.9}{2} = 0.95. So we have T = 1.7291

The margin of error is:

M = T\frac{s}{\sqrt{n}}

In which s is the standard deviation of the sample and n is the size of the sample. For this question, we have s = 5, n = 20. So

M = T\frac{s}{\sqrt{n}}

M = 1.7291\frac{5}{\sqrt{20}}

M = 1.933

The margin of error of the 90% confidence interval of a student's average typing speed is of 1.933 wpm.

8 0
3 years ago
Jan has a piece of yarn that is 6 1/2 feet long. She cuts off a piece that is 2 5/12 feet long. How much yarn does she have left
icang [17]
The answer is b because all you have to do is just subtract if I am wrong so sorry
5 0
2 years ago
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