Please help :) thanks !

If the heights of 300 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches, how many studen

Lunna [17]

Given:
μ = 68 in, population mean
σ = 3 in, population standard deviation

Calculate z-scores for the following random variable and determine their probabilities from standard tables.

x = 72 in:
z = (x-μ)/σ = (72-68)/3 = 1.333
P(x) = 0.9088

x = 64 in:
z = (64 -38)/3 = -1.333
P(x) = 0.0912

x = 65 in
z = (65 - 68)/3 = -1
P(x) = 0.1587

x = 71:
z = (71-68)/3 = 1
P(x) = 0.8413

Part (a)
For x > 72 in, obtain
300 - 300*0.9088 = 27.36

Answer: 27

Part (b)
For x ≤ 64 in, obtain
300*0.0912 = 27.36

Answer: 27

Part (c)
For 65 ≤ x ≤ 71, obtain
300*(0.8413 - 0.1587) = 204.78

Answer: 204

Part (d)
For x = 68 in, obtain
z = 0
P(x) = 0.5
The number of students is
300*0.5 = 150

Answer: 150

3 0

3 years ago

How do I evaluate 8^7 / 8^7?

morpeh [17]

Answer:

The final result is 1

Step-by-step explanation:

Remember the following:

$\frac{x^{m}}{x^{n}} = x^{m-n} \\$

And that x^0= 1

We have: 8^7 / 8^7= 8 ^ (7-7)=8^0=1

3 0

3 years ago

) A coin collection consisting of pennies, dimes, and quarters totals 45 coins. The number of

Sloan [31]

9514 1404 393

Answer:

$7.14

Step-by-step explanation:

Let p, d, q represent the numbers of pennies, dimes, and quarters in the collection, respectively.

p + d + q = 45 . . . . . . . . there are 45 coins in the collection

2p +5 = q . . . . . . . . . . . . 5 more than twice the number of pennies

p + 4 = d . . . . . . . . . . . . . 4 more than the number of pennies

Substituting the last two equations into the first gives ...

p +(p +4) +(2p +5) = 45

4p = 36 . . . . . . . . . . . . . subtract 9

p = 9 . . . . . . . . . . . divide by 4

d = 9 +4 = 13

q = 2(9) +5 = 23

The value of the collection is ...

23(0.25) +13(0.10) +9(0.01) = 5.75 +1.30 +0.09 = 7.14

The coin collection is worth $7.14.

5 0

3 years ago

Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10. Rectangle C has length 30 and width 15.

Anna007 [38]

Answer:

yes; 1.25

Step-by-step explanation:

The length to width ratios of the rectangles are ...

A: 12/8 = 1.5

B: 15/10 = 1.5

C: 30/15 = 2.0

__

Rectangles A and B have the same aspect ratio, so are similar. Rectangle B is a scaled copy of A with a scale factor of 10/8 = 1.25.

7 0

4 years ago

A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) rep

prohojiy [21]

The sketch of the parabola is attached below

We have the focus $(a,b) = (2, -0.5)$
The point $P(x,y)$
The directrix, c at $y=-1.5$

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; $(2, -0.5)$ and $(x,y)$ .
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$

Step 2
Find the distance between the point P to the directrix $c$ . It is a vertical distance between y and c, expressed as $y-c$

Step 3
The equation of parabola is then given as
$\sqrt{ (x-a)^{2}+ (y-b)^{2} }$ = $y-c$
$(x-a)^{2}+ (y-b)^{2}= (y-c)^{2}$ ⇒ substituting a, b and c
$(x-2)^{2}+ (y--0.5)^{2} = (y--1.5)^{2}$
$(x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2}$ ⇒Rearranging and making $y$ the subject gives

$y= \frac{ x^{2} }{2} -2x+1$

7 0

4 years ago