We saw two distributions for triathlon times: n(μ= 4313,σ=583) formen, ages 30 - 34andn(μ= 5261,σ= 807) for thewomen, ages 25 - 29group. times are listedin seconds. use this information to compute each of the following:
(a) the cutoff time for the fastest 5% of athletes in the men’s group, i. e. those who took the shortest 5%of time to finish.
(b) the cutoff time for the slowest 10% of athletes in the women’s group.

a) 3353.965 seconds

b) 6295.574 seconds

Step-by-step explanation:

(a) The cutoff time for the fastest 5% of athletes in the men’s group

Let X be the cut-off time for the fastest 5% of athletes in the men's group and be the corresponding z-score of X in the distribution             N(μ= 4313,σ=583).

Then P(z<)=0.05 and =-1.645

z score can be calculated using the formula

=1.645= where

putting the numbers in the formula we get

-1.645= , solving for X in the equation we get

X=3353.965

(b) The cutoff time for the slowest 10% of athletes in the women’s group

Let Y be the cut-off time for the slowest 10% of athletes in the women's group and be the corresponding z-score of Y in the distribution N(μ= 5261,σ= 807).

Then P(z<)=0.90 and  =1.282

Using the above formula

putting the numbers in the formula we get

1.282= , solving for Y in the equation we get

Y=6295.574

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions