Two cyclists start at the same point and travel in opposite directions. One cyclist travels 5 faster than the other. If the two
1 answer:
You might be interested in
Answer: Hello the lengths of the pieces of wood is missing but I will provide the format for drawing a line plot which you can now plug in your own values .
answer :
First draw a number line containing all the values in the given data set
Place a dot on top every value contained in the given data set
place as many dots as possible representing the frequency of the value in the given dataset
Step-by-step explanation:
A line plot is simply a method of displaying given data on a number line
steps :
First draw a number line containing all the values in the given data set
Place a dot on top every value contained in the given data set
place as many dots as possible representing the frequency of the value in the given dataset
attached below is an example
Answer:
a) 0.7088 = 70.88% probability that a randomly selected President was less than 60 years old on the day of their first inauguration.
b) The 75th percentile for the age of United States Presidents on the day of inauguration is 61.
c) 0.8643 = 86.43% probability that the average age on the day of their first inauguration for a random sample of 4 United States Presidents exceeds 60 years.
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.
The age of United States Presidents on the day of their first inauguration follows a Normal distribution with mean 56 and standard deviation 7.3.
This means that
(a) (5 points) Compute the probability that a randomly selected President was less than 60 years old on the day of their first inauguration.
This is the pvalue of Z when X = 60. So
has a pvalue of 0.7088
0.7088 = 70.88% probability that a randomly selected President was less than 60 years old on the day of their first inauguration.
(b) (5 points) Compute the 75th percentile for the age of United States Presidents on the day of inauguration.
This is X when Z has a pvalue of 0.75. So X when Z = 0.675.
The 75th percentile for the age of United States Presidents on the day of inauguration is 61.
(c) (5 points) Compute the probability that the average age on the day of their first inauguration for a random sample of 4 United States Presidents exceeds 60 years.
Now, by the Central Limit Theorem, we have that
This is the pvalue of Z when X = 60. So
By the Central Limit Theorem
has a pvalue of 0.8643
0.8643 = 86.43% probability that the average age on the day of their first inauguration for a random sample of 4 United States Presidents exceeds 60 years.