Mathematics, 18.03.2020 17:26 cdavis379

Suppose the time to complete a 200-meter backstroke swim for female competitive swimmers is normally distributed with a mean μ = 141 seconds and a standard deviation σ = 7 seconds.
Now suppose the fastest 6% of female swimmers in the nation are offered college scholarships. In order to be given a scholarship, a swimmer must complete the 200-meter backstroke in no more than how many seconds?
Give your answer in whole numbers.

Answers: 1

Show answers

Answers

Answer from: pennygillbert

The swimmer must complete the 200-meter backstroke in no more than 130 seconds.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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.

In this problem, we have that:

$\mu = 141, \sigma = 7$

Fastest 6%

At most in the 6th percentile, that is, at most a value of X when Z has a pvalue of 0.07. So we have to find X when Z = -1.555.

$Z = \frac{X - \mu}{\sigma}$

$-1.555 = \frac{X - 141}{7}$

X - 141 = -1.555*7

X = 130

The swimmer must complete the 200-meter backstroke in no more than 130 seconds.

Answer from: Quest

step-by-step explanation:

a. since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since 2010 0 1 2 3 4 5

profits made in 1000's 39 84 111 120 111 84

we find that profit gradually increases form 2010 to 2013 upto 120, then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a. since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

Another question on Mathematics

Mathematics, 21.06.2019 15:00

Prove that 3: 8 is equivalent to 12: 32.a. use diagrams to support your answer.

Answers: 1

Answer

Mathematics, 21.06.2019 17:20

What other information do you need to prove triangle dac=bca by asa

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y > 2x + 3y is less than negative 3 over 2 times x minus 4part a: describe the graph of the system, including shading and the types of lines graphed. provide a description of the solution area. (6 points)part b: is the point (â’4, 6) included in the solution area for the system? justify your answer mathematically. (4 points)

Answers: 1

Answer

Mathematics, 22.06.2019 01:10

To find the inverse of a number a, one can use the equation f(c) = a-1/c=0 where c is the inverse of a use the secant method of finding roots of equations to find the inverse of a = 2.5 ,er = 0.001%

Answers: 3

Answer

You know the right answer?

Suppose the time to complete a 200-meter backstroke swim for female competitive swimmers is normally...

Questions