Answer:
C.20
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
The margin of error is the difference between the two bounds, divided by 2.
In this question:
Lower bound: 70
Upper bounf: 110
Margin of error:
Thus the correct answer is given by option C.
Answer:
a. 0.9931
b. 0.3423
c. 0.3907
d. 0.2670
e. 3.15
f. 1.0796
Step-by-step explanation:
The probability of the variable that said the number of left-handed people follow a Binomial distribution, so the probability is:
nCx is calculated as:
Where x is the number of left-handed people, n is the number of people selected at random and p is the probability that a person is left--handed. So P(x) is:
Then the probabilities P(0), P(1), P(2), P(3), P(4) and P(5) are:
Then, the probability P(x≥1) that there are some lefties among the 5 people is:
P(x≥1) = P(1) + P(2) + P(3) + P(4) + P(5)
P(x≥1) = 0.0590 + 0.2011 + 0.3423 + 0.2914 + 0.0993 = 0.9931
The probability P(3) that there are exactly 3 lefties in the group is:
P(3) = 0.3423
The probability P(x≥4) that there are at least 4 lefties in the group is:
P(x≥4) = P(4) + P(5) = 0.2914 + 0.0993 = 0.3907
The probability P(x≤2) that there are no more than 2 lefties in the group is:
P(x≤2) = P(0) + P(1) + P(2) = 0.0069 + 0.0590 + 0.2011 = 0.2670
On the other hand, the expected value E(x) and standard deviation S(x) of the variable that follows a binomial distribution is: