Answer: The expected value of the water depth is 4.5 m.
Step-by-step explanation:
Let x be a random variable which is uniformly distributed in interval [a,b] .
Then the mean of the distribution is ghiven by :-
Given : While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.
Then, the expected value of the water depth =
Hence, the expected value of the water depth is 4.5 m.
Answer:
<h3>-5(2q - 3)</h3>Step-by-step explanation:
Answer:
83.89% probability that the sample mean would be greater than 98.8 gallons
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central 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 random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation, which is also called standard error
In this problem, we have that:
The standard deviation is the square root of the variance. So
If 44 racing cars are randomly selected, what is the probability that the sample mean would be greater than 98.8 gallons
This probability is 1 subtracted by the pvalue of Z when X = 98.8. So
By the Central Limit Theorem
has a pvalue of 0.1611
1 - 0.1611 = 0.8389
83.89% probability that the sample mean would be greater than 98.8 gallons
Answer:
Some details are missing in the question, here are the details ; A proton initially has v = -6.5i + 17j + 13k and then 8.00s later has v = -2.8i + 17j - 9.3k (in meters per seconds).
a) proton's average acceleration in unit vector notation = 0.46i - 2.78k
b) Magnitude = 2.85m/s2
c) angle between and the positive direction of the x axis = 279.39 degree (counter clockwise)
Step-by-step explanation:
The detailed and step by step explanation is as shown in the attachment
