During his hike milt drank 1 liter of water and 1 liter of sports drink how many milliliters of liquid did he drink
1 answer:
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Answer:
8.68 seconds
Step-by-step explanation:
Given:
Height of the deck above the street, s = 370 m
Since the condition is of free falling
thus,
initial speed, u = 0
Acceleration of the penny = acceleration due to gravity, g = 9.81 m/s²
Now,
from Newton's equation of motion, we have
here,
s is the distance
a is the acceleration
t is the time
on substituting the values, we get
or
t² = 75.433
or
t = 8.68 seconds
Answer:
The probability of the sample mean foot length less than 23 cm is 0.120
Step-by-step explanation:
* Lets explain the information in the problem
- The eighth-graders asked to measure the length of their right foot at
the beginning of the school year, as part of a science project
- The foot length is approximately Normally distributed, with a mean of
23.4 cm
∴ μ = 23.4 cm
- The standard deviation of 1.7
∴ σ = 1.7 cm
- 25 eighth-graders from this population are randomly selected
∴ n = 25
- To find the probability of the sample mean foot length less than 23
∴ The sample mean x = 23, find the standard deviation σx
- The rule to find σx is σx = σ/√n
∵ σ = 1.7 and n = 25
∴ σx = 1.7/√25 = 1.7/5 = 0.34
- Now lets find the z-score using the rule z-score = (x - μ)/σx
∵ x = 23 , μ = 23.4 , σx = 0.34
∴ z-score = (23 - 23.4)/0.34 = -1.17647 ≅ -1.18
- Use the table of the normal distribution to find P(x < 23)
- We will search in the raw of -1.1 and look to the column of 0.08
∴ P(X < 23) = 0.119 ≅ 0.120
* The probability of the sample mean foot length less than 23 cm is 0.120
Answer:
a) 99% of the sample means will fall between 0.933 and 0.941.
b) By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be 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.
(a) If the true mean is 0.9370 with a standard deviation of 0.0090 within what interval will 99% of the sample means fail?
Samples of 34 means that
We have that
By the Central Limit Theorem,
Within what interval will 99% of the sample means fail?
Between the (100-99)/2 = 0.5th percentile and the (100+99)/2 = 99.5th percentile.
0.5th percentile:
X when Z has a pvalue of 0.005. So X when Z = -2.575.
By the Central Limit Theorem
99.5th percentile:
X when Z has a pvalue of 0.995. So X when Z = 2.575.
99% of the sample means will fall between 0.933 and 0.941.
(b) If the true mean 0.9370 with a standard deviation of 0.0090, what is the sampling distribution of ¯X?
By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.