X ÷ 8 = 8a: 16b: 56c: 62d: 64
2 answers:
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Answer:
24% of those surveyed liked neither
Step-by-step explanation:
Set concepts:
We use set concepts to solve this question.
I am going to say that:
P(A) is the percentage of people that liked to swim.
P(B) is the the percentage of people that liked to run.
The percentage of people that liked at least one of these activities is:
In which is the probability that a person liked both these activities.
The percentage of people that liked neither is:
Of those surveyed, 58% said they liked to swim and 36% said they liked to run.
This means that
18% said they liked both swimming and running
This means that
What percent of those surveyed liked neither?
At least one:
Neither:
24% of those surveyed liked neither
Answer:
0.1739 = 17.39% probability that the cab actually was blue
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Witness asserts the cab is blue.
Event B: The cab is blue.
Probability of a witness assessing that a cab is blue.
20% of 95%(yellow cab, witness assesses it is blue).
80% of 5%(blue cab, witness assesses it is blue). So
Probability of being blue and the witness assessing that it is blue.
80% of 5%. So
What is the probability that the cab actually was blue?
0.1739 = 17.39% probability that the cab actually was blue
Answer:
Step-by-step explanation:
Hello!
The variable of interest is
X: production cost of a major move
Its average is μ= 65 million dollars, and standard deviation σ= 18 million dollars.
a)
This variable has a normal distribution X~N(μ;σ²)
X~N(65;324)
b)
The distribution of the sample mean has the same shape as the distribution of the variable, but its variance is affected by the sample size:
~N(μ;σ²/n) ⇒
~N(65;8.3077)
σ²/n= 324/39= 8.30769≅ 8.3077
c)
You have to calculate the probability of a single movie costing between 69 and 66 million dollars, symbolically:
P(66≤X≤69)= (X≤69)-P(X≤66)
You have to use the standard normal distribution to calculate this probability, so first you have to calculate the Z values that correspond to each value of X using: Z= (X-μ)/σ ~ N(0;1)
Z₁= (69-65)/18= 0.22
Z₂=(66-65)/18= 0.05
Now you look for the corresponding probability values using the standard normal table
P(Z≤0.22)= 0.58706
P(Z≤0.05)= 0.51994
P(66≤X≤69)= (X≤69)-P(X≤66)
P(Z≤0.22)-P(Z≤0.05)= 0.58706 - 0.51994= 0.06712
d)
Now you have to calculate the probability of the average production cost to be between 69 and 66 million. Since the probability is for the average value of the sample, you have to work using the distribution of the sample mean. The values od Z are to be calculated using the formula Z= (-μ)/(σ/√n)
σ/√n= 2.8823
P(66≤≤69)= (
≤69)-P(
≤66)
Z₁= (69-65)/2.8823= 1.387= 1.39
Z₂= (66-65)/2.8823= 0.346= 0.35
P(Z≤1.39)-P(Z≤0.35)= 0.91774 - 0.63683= 0.28091
e)
No
If the variable has an unknown or non-normal distribution, but the sample is large enough (normally a sample n≥30 is considered to be large) you can apply the central limit theorem and approximate the sampling distribution to normal.
I hope this helps!