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True [87]
3 years ago
5

You entered a contest through your local television station. There is one first prize of a new car! There are 5 second place pri

zes of $1000, and 20 third place prizes of $100. If there are 2000 entries, what is the chance that you will win one of the 2nd place prizes?
Mathematics
2 answers:
Grace [21]3 years ago
8 0

Answer:

\frac{1}{400} or 0.0025 0r 0.25%

Step-by-step explanation:

There are three categories that will get a prize

1) First place = 1 person

2) Second place = 5 persons

3) Third place = 20 persons

A total of 26 people will get prizes.

However, we want to determine your chance to win one of the second place prizes

There are 5 prizes in second place

This means out of a total of 2000 people, you could be among the 5

i.e 5 out of 2000

This is \frac{5}{2000} = \frac{1}{400} = 0.0025

This means you have a chance of 1 out of 400

= 0.25%

Helga [31]3 years ago
8 0
There are 26 people who will get the chance to get first, second, or third place. But, you need to focus on the 5 second place prizes. The chance that you will win a second place prize is 5 to 2000, or, simplified, is a 1 to 400 chance. In a percent, that would be a 0.25% chance that you will win one of the second place prizes. Hope I helped :)
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The probability that the SRS of 10 students will spend an average of between 600 and 700 dollars is 0.8132.

Let x be the total amount spent by students.

x follows normal distribution with mean μ = 650,

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We take a simple random sample of size n = 10

We are asked to find average spending of 10 students ( x ) is between 600 and 700

We have to find P( 600 <= x <= 700)

According to the sampling distribution of the sample mean x, it follows an approximately normal distribution with mean μ{x} = μ and standard deviation  δ{x} = {δ}/{√n}

Therefore here mean of x,( μ{x} ) = 650 and

standard deviation of x, δ{x} = {120}/{√10} = 37.9473

The probability that the SRS of 10 students will spend an average of between 600 and 700 dollars is,

Let Z= x - μ / δ

Z₁ = 600 - 650 / 37.9473 = -1.32 similarly

Z₂ = 700 - 650 / 37.9473 = 1.32

From standard normal distribution table, P( -1.32 <  x  <  1.32) = 0.8132

The probability that the SRS of 10 students will spend an average of between 600 and 700 dollars is 0.8132

To learn more about Normal distribution click here:

brainly.com/question/15103234

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