The table represents an exponential function. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4
1 answer:
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Answer:
a) P(12.99 ≤ X ≤ 13.01) = 0.3840
b) P(X ≥ 13.01) = 0.3075
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the cental limit theorem.
Normal probability distribution
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
(a) Calculate P(12.99 ≤ X ≤ 13.01) when n = 16.
Here we have
This probability is the pvalue of Z when X = 13.01 subtracted by the pvalue of Z when X = 12.99.
X = 13.01
By the Central Limit Theorem
has a pvalue of 0.6915
X = 12.99
has a pvalue of 0.3075
0.6915 - 0.3075 = 0.3840
P(12.99 ≤ X ≤ 13.01) = 0.3840
(b) How likely is it that the sample mean diameter exceeds 13.01 when n = 25?
P(X ≥ 13.01) =
This is 1 subtracted by the pvalue of Z when X = 13.01. So
has a pvalue of 0.6915
1 - 0.6915 = 0.3075
P(X ≥ 13.01) = 0.3075
The equivalent scales are:
3 cm to 15 km is equivalent to 1 cm to 5 km ⇒ answer A
5 mm to 2.5 km is equivalent to 1 cm to 5 km ⇒ answer D
1 mm to 500 m is equivalent to 1 cm to 5 km ⇒ answer E
Step-by-step explanation:
To solve this problem do that
1. The given scale is 1 cm represents 5 km, then all given answer must
be change to cm and km
2. Find the equivalent scales to the given scale
A.
∵ 3 cm represents 15 km
- Divide both of them by 3
∴ 1 cm represents 5 km
3 cm to 15 km is equivalent to 1 cm to 5 km
B.
∵ 1 mm represents 150 km
- Change mm to cm
∵ 1 cm = 10 mm
∴ 1 mm = cm = 0.1 cm
∴ 0.1 cm represents 150 km
- Multiply both by 10
∴ 1 cm represents 1500 km
1 mm to 150 km is not equivalent to 1 cm to 5 km
C.
∵ 5 cm represents 1 km
- Divide both my 5
∴ 1 cm represents 0.2 km
5 cm to 1 km is not equivalent to 1 cm to 5 km
D.
∵ 5 mm represents 2.5 km
- Change mm to cm
∵ 1 cm = 10 mm
∴ 5 mm = cm = 0.5 cm
∴ 0.5 cm represents 2.5 km
- Divide both by 0.5
∴ 1 cm represents 5 km
5 mm to 2.5 km is equivalent to 1 cm to 5 km
E.
∵ 1 mm represents 500 m
- Change mm to cm
∵ 1 cm = 10 mm
∴ 1 mm = cm = 0.1 cm
- Change m to km
∵ 1 km = 1000 m
∴ 1 m = = 0.001 km
∴ 500 m = = 0.5 km
∴ 0.1 cm represents 0.5 km
- Multiply both by 10
∴ 1 cm represents 5 km
1 mm to 500 m is equivalent to 1 cm to 5 km
Learn more:
You can learn more about the equivalent quantities in brainly.com/question/120752
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