Answer:n=5
Step-by-step explanation:
+8 to both sides to remove the eight -3+8=five the only things left are n and 5 so n=5
Given:
p = 90% = 0.9, the probability that an adult has had chickenpox by age 50.
Therefore,
q = 1 - p = 0.1, the probability that an adult has not had chickenpox by age 50.
Part (a)
Because there are only two answers: "Yes" or "No" to whether an adult has had chickenpox by age 50, the use of the binomial distribution is justified.
Part (b):
Calculate the probability that exactly 97 out of 100 sampled adults have had chickenpox.
The probability is
P₁ = ₁₀₀C₉₇ (0.9)⁹⁷ (0.1)³ = 0.0059
Answer: 0.006 or 0.6%
Part (c)
Calculate the probability that exactly 3 adults have not had chickenpox.
Theis probability is equal to
P₂ = 1 - P₁ = 1 - 0.006 = 0.994
Answer: 0.994 or 99.4%
Part (d)
Calculate the probability that at least 1 out of 10 randomly selected adults have had chickenpox.
The probability is
P₃ = ₁₀C₀ (0.9)⁰ (0.1)¹⁰ + ₁₀C₁ (0.9)¹ (0.1)⁹ = 10⁻¹⁰ + 10⁻⁹ = 10⁻⁹ ≈ 0
Answer: 0
Part (e)
Calculate the probability that at most 3 out of 10 randomly selected adults have not had chickenpox.
The probability is
P₄ = 1 - [₁₀C₀ (0.9)⁰(0.1)¹⁰ + ₁₀C₁ (0.9)¹(0.1)⁹ + ₁₀C₂ (0.9)²(0.1)⁸ + ₁₀C₃ (0.9)³(0.1)⁷]
= 1 - (10⁻¹⁰ + 9 x 10⁻⁹ + 3.645 x 10⁻⁷ + 8.748 x 10⁻⁶)
= 1
Answer: 1.0 or 100%
21. In an election involving only two candidates, every vote will be counted against one candidate or the other. The total of votes for the two candidates must add to the total of votes cast. The numbers 60% and 1/3 = 33 1/3% add to 93 1/3%, not 100%, so cannot be right.
22. 500/2000 = 1/4 (fraction) = 0.25 (decimal) = 25%
... 1200/2000 = 3/5 (fraction) = 0.60 (decimal) = 60%
... 300/2000 = 3/20 (fraction) = 0.15 (decimal) = 15%
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The ratio of each number to 2000 gives you the fraction. You need to reduce it by removing common factors from numerator and denominator. Some calculators will do this for you. You can start by removing an equal number of zeros from numerator and denominator, for example 500/2000 = 5/20. Then you make use of your knowledge of multiplication tables to identify and remove any additional common factors. In this example, 5/20 = 5/(5·4) = 1/4.
The decimal form can be found a couple of ways. One is to simply recognize the decimal form of the fraction you have. (You have memorized that 1/4 = 0.25, for example.) Another is to multiply numerator and denominator by a number that makes the denominator be a power of 10, such as 100. For example, 1/4 = (1·25)/(4·25) = 25/100. Now, you use place value to put this fraction into decimal form. Twenty-five hundredths is 0.25.
Yet another way to find the decimal value of a fraction is to divide the numerator by the denominator using long division (or your calculator).
If you have done the decimal part by making a denominator of 100, you have already found the percentage. The "%" symbol means "/100", so 25/100 is 25%. They are two ways of writing the same thing.
Moving the decimal point two places to the right and adding a "%" sign is another way to get to a percentage from a decimal. (0.463 = 46.3%, for an example not related to this problem.)
Answer:
13/25 is greater
Step-by-step explanation:
As
50% = 50/100 = 0.5
And
13/25 = 0.52
S0 0.5 < 0.52
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