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Montano1993 [528]
3 years ago
9

At Camp Roan, 70% of the kids are taking horseback riding lessons. If 210 kids are taking horseback riding lessons, how many kid

s are at Camp Roan altogether?
Mathematics
1 answer:
babymother [125]3 years ago
4 0

Answer:

total kids in the camp = 300

Step-by-step explanation:

let the number of kids in the camp be x

from the above situation, we get

=》70% of all kids in the camp is 210

=》

\frac{70}{100}  \times x = 210

=》

x =  210 \times  \frac{100}{70}

=》

x = 3 \times 100

=》

x = 300

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Answer and Explanation:

Given : The random variable x has the following probability distribution.

To find :

a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.

b. Calculate the expected value of x.

c. Calculate the variance of x.

d. Calculate the standard deviation of x.

Solution :

First we create the table as per requirements,

x      P(x)         xP(x)           x²            x²P(x)

0    0.25           0               0                0

1     0.20        0.20             1              0.20

2    0.15          0.3               4             0.6

3    0.30         0.9               9             2.7

4    0.10          0.4               16             1.6

   ∑P(x)=1     ∑xP(x)=1.8               ∑x²P(x)=5.1

a) To determine that table shows a probability distribution we add up all five probabilities if the sum is 1 then it is a valid distribution.

\sum P(X)=0.25+0.20+0.15+0.30+0.10

\sum P(X)=1

Yes it is a probability distribution.

b) The expected value of x is defined as

E(x)=\sum xP(x)=1.8

c) The variance of x is defined as

V=\sum x^2P(x)-(\sum xP(x))^2\\V=5.1-(1.8)^2\\V=5.1-3.24\\V=1.86

d) The standard deviation of x is  defined as

\sigma=\sqrt{V}

\sigma=\sqrt{1.86}

\sigma=1.136

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Answer:

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LA: it’s supposed to be 1040cm???

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