Ask question

Ask question

All categories

3 years ago

8

g The distribution of heights of 7-year-old girls is approximately normally distributed with a mean of 47.7 inches and a standar

d deviation of 2.4 inches. Amy is 7 years old, and her height is 1.34 standard deviations above the mean. Her friend Sophia is also 7 years old and is at the 94th percentile of the height distribution. a. At what percentile is Amy's height? Draw and label the Normal model that corresponds to this situation. b. How does her height compare to Sophia's? c. What percent of 7-year-old girls would you expect to be taller than 49.4 inches? Draw and label the Normal model that corresponds to this situation. d. Below what height are the shortest 30% of 7-year-old girls? Draw and label the Normal model that corresponds to this situation.

1 answer:

Lana71 [14]3 years ago

6 0

Answer:

a) 90th percentile

b) X = 51.43 ( Sophia's height ) , Amy's height = 50.92

c) 0.2394

d) 46.44 inches

Step-by-step explanation:

mean value( <em>u</em> ) = 47.7 inches

std ( σ )= 2.4 inches

Amy height = 1.34 std above mean value

Sophia height = 94th percentile of height distribution

A ) what percentile is Amy's height

To Calculate the percentile of Amy's height

P( X ≤ 50.916 ) = P( (X-µ)/σ ) ≤ (50.916-47.7) /2.4)

=P(Z ≤ 1.340 ) = 0.9099 = 90th percentile

B) How Amy's height compare to Sophia's

The proportion given based on Sophia's height = 0.94

z -value at the proportion ( 0.94 ) = 1.55 ( from excel )

note z-value can be calculated using = ( x - µ ) / σ

therefore: X (Sophia's height ) = zσ + µ= (1.55 * 2.4) + 47.7

X = 51.43 ( Sophia's height ) , Amy's height = 50.92

C) percentage expected to be taller than 49.4 inches

P ( X ≥ 49.40 ) = P( (X-µ)/σ) ≥ (49.4-47.7) / 2.4)

= P(Z ≥ 0.708 )

= P( Z < -0.708 )

= 0.2394

D) Below what height are the shortest 30% of 7-year old girls

( <em>u</em> ) = 47.7 inches

std ( σ )= 2.4 inches

given proportion = 30% = 0.3

The z value at 0.3 = -0.52 ( from excel )

to calculate for X ( height ) we have to apply the formula used to determine z value

z= (x-µ) /σ

hence : X = (Z * σ) +<em> u = </em>(-0.52 * 2.4 ) + 47.7

X = 46.44

below 46.44 inches lies about 30% of 7 year old girls height

You might be interested in

The riding stables just received an unexpected rush of registrations for the next horse show, and quickly needs to create some a

liraira [26]

Answer:

Maximum added area will be 60,000 ft²

Each paddock measure 200 ft by 150 ft, and the paddocks share a 200-ft long side.

Step-by-step explanation:

Consider the provided information.

There is sufficient funding to rent 1200 feet of temporary chain-link fencing.

The plan is to form two paddocks with one shared fence running down the middle.

The total length of fencing is 1200 feet that is same as the total perimeter including that shared line down the middle.

Therefore, the perimeter is

$P = 1200 = 2L + 3w$

Solve for L

$1200-3w = 2L$

$L=600-\frac{3w}{2}$

As we know the area of rectangle is A=L×W

Substitute the value of L in above formula.

$A=(600-\frac{3w}{2})\times w\\A=600w-\frac{3w^2}{2}$

$A=-\frac{3w^2}{2}+600w$

The above equation makes a downward parabola.

In order to find the maximum, find the vertex of parabola as shown:

$W=\frac{-b}{2a}=\frac{600}{2\times\frac{3}{2}}=200$

Hence, the width should be 200 ft in order to get maximum area,

Therefore, the length will be:

$1200 = 2L + 3(200)$

$L=300$

Now substitute the value of L and W in area formula.

A=300×200=60,000

Hence, maximum added area will be 60,000 ft²

Hence, the length should be 300 ft, and each paddock should then be 150 feet long.

Each paddock measure 200 ft by 150 ft, and the paddocks share a 200-ft long side.

5 0

3 years ago

I’m having trouble doing this one can someone finish the rest

kolbaska11 [484]

Answer:

2

Step-by-step explanation:

12-2=m(2+3)

m=10/5=2

m=2

6 0

3 years ago

Read 2 more answers

Sean used the $1,200 he got from his graduation party to open a savings account. If the account earns 1% interest each month and

Greeley [361]

Answer:

$\$1,920$

Step-by-step explanation:

we know that

The simple interest formula is equal to

$A=P(1+rt)$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

in this problem we have

$t=5*12=60\ months\\ P=\$1,200\\r=0.01$

substitute in the formula above

$A=\$1,200(1+0.01*60)$

$A=\$1,200(1.6)=\$1,920$

6 0

2 years ago

Plz help with math thank you

Delicious77 [7]

Answer:

Step-by-step explanation:

Law of Sines recall Sin(A) /a = Sin(B) /b

does the above make sense?

Next we need to find the angle of A

notice that 16+75=91 :o

so angle A is only 89° ..(b/c all the way around then inside of a triangle is 180) so this is NOT a right triangle but that's okay, b/c law of sines still works fine.

then we want to find length of line AB

and if 89 = A then a = BC

and if 75 = B the b = AB (note that in the given triangle this is angle C, i'm using B , b/c you can see the difference between capital B and lower case b much easier than you can with C, & c :/ )

capitals are the angles while lower case are the length of the sides

then

Sin(89) / 29 = Sin(75) / b

solve the parts that can be put into numbers or solve for 'b' first, that means isolate 'b' all by itself on one side of the equal sign .

0.034477 = 0.965925/ b

b = 0.965925 / 0.034477

b = 28.0165

b = 28.0 ( to the nearest 10th)

we have the parts to plug in now

Sin(75) /

8 0

3 years ago

Solve for the given variable

Ne4ueva [31]

Answer:

30

Step-by-step explanation:

Well we know the first angle is 90 degrees, which means we have 90 degrees left to work with. Then, the top angle would be 60 degrees, because there is a straight line (which of course has to equal 180), so 180-120 = 60. Now, 90-60=30!

3 0

2 years ago

Read 2 more answers