What percentage of the population has a heart rate between 68 and 77

49.87% of the population has a heart rate between 68 and 77.

Step-by-step explanation:

We are given that the mean of the data for the resting heart of adults is 68 beats per minute and the standard deviation is 3 beats per minute.

Let X = the data for the resting heart of adults

The z-score probability distribution for the normal distribution is given by;

                          Z  =    ~ N(0,1)

where, = population mean = 68 beats per minute

            = standard deviation = 3 beats per minute

Now, the percentage of the population that has a heart rate between 68 and 77 is given by = P(68 < X < 77)

    P(68 < X < 77) = P(X < 77) - P(X 68)

    P(X < 77) = P( < ) = P(Z < 3) = 0.9987

    P(X 68) = P( ) = P(Z 0) = 0.50

The above probability is calculated by looking at the value of x = 3 and x = 0 in the z table which has an area of 0.9987 and 0.50 respectively.

Therefore, P(68 < X < 77) = 0.9987 - 0.50 = 0.4987 or 49.87%

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.