Tyra is training for a bicycle race. Each week she rides a total distance greater than 10 km and less than or equal to 30 km. If
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Answer:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Solution to the problem
For this case we select a sample of n =100
From the central limit theorem we know that the distribution for the sample mean is given by:
So then the sample mean would be:
And the standard deviation would be:
From the table, the speed of Corinne is given by
From the graph, the speed of Aretha is given by
The distance from the starting point of Corinne at any time t is given by D = 0.125t while the distance from the starting point of Aretha at any time t is given by D = 3.5 + 0.1t
Let t be the number of minutes after the start of the race when Corinne catchs Aretha, then
0.125t = 3.5 + 0.1t
0.025t = 3.5
t = 3.5 / 0.025 = 140
Therefore, the number of <span>minutes after the start of the race that Corinne will catch Aretha</span> is 140 minutes.
From the graph, the speed of Aretha is given by
The distance from the starting point of Corinne at any time t is given by D = 0.125t while the distance from the starting point of Aretha at any time t is given by D = 3.5 + 0.1t
Let t be the number of minutes after the start of the race when Corinne catchs Aretha, then
0.125t = 3.5 + 0.1t
0.025t = 3.5
t = 3.5 / 0.025 = 140
Therefore, the number of <span>minutes after the start of the race that Corinne will catch Aretha</span> is 140 minutes.
Answer:Answer:a) Area=f(x)= 24x-x^2
b) f(x) ranges from 0 to 144
c) Area max = 144 ft^2
Step-by-step explanation: shown in the attachment
