Billy fills a crate with equal-sized cubes. The volume of each cube is exactly 1 cubic foot. He can fit 7 cubes across the lengt
1 answer:
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Answer:
C) I & III
Step-by-step explanation:
Given:
Sample size, n = 18
Sample proportion = 25% = 0.25
Here, a random sample of 18 adults were chosen from the 1500 adults in town. This shows that the random condition was satisfied because the sample was drawn randomly from the general population of adults in the town.
For the normal condition to be satisfied, np should be greater than 10, ie np > 10.
In this case, np = 18 * 0.25 = 4.5
Since np is less than 10, the normal condition was not satisfied.
For the 10% condition to be satisfied, sample size should not be more than 10% of the general population.
Here, the sample size is 18 and the population is 1500. Therefore,
Since the sample size is 1.2% of the population which is less than 10%, the 10% condition was satisfied.
The correct option is C, because only I & III were satisfied.
Answer:
a) 0.5.
b) 0.8413
c) 0.8413
d) 0.6826
e) 0.9332
f) 1
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
(a) P(x > 6) =
This is 1 subtracted by the pvalue of Z when X = 6. So
has a pvalue of 0.5.
1 - 0.5 = 0.5.
(b) P(x < 6.2)=
This is the pvalue of Z when X = 6.2. So
has a pvalue of 0.8413
(c) P(x ≤ 6.2) =
In the normal distribution, the probability of an exact value, for example, P(X = 6.2), is always zero, which means that P(x ≤ 6.2) = P(x < 6.2) = 0.8413.
(d) P(5.8 < x < 6.2) =
This is the pvalue of Z when X = 6.2 subtracted by the pvalue of Z when X 5.8.
X = 6.2
has a pvalue of 0.8413
X = 5.8
has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
(e) P(x > 5.7) =
This is 1 subtracted by the pvalue of Z when X = 5.7.
has a pvalue of 0.0668
1 - 0.0668 = 0.9332
(f) P(x > 5) =
This is 1 subtracted by the pvalue of Z when X = 5.
has a pvalue of 0.
1 - 0 = 1