1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
umka2103 [35]
3 years ago
7

Navy PilotsThe US Navy requires that fighter pilots have heights between 62 inches and78 inches.(a) Find the percentage of women

meeting the height requirement.(b) Find the percentage of men meeting the height requirement.(c) If the height requirements are changed to exclude the tallest 10% of men and the shortest10% of women, what are the new height requirements?

Mathematics
1 answer:
Zigmanuir [339]3 years ago
7 0

The first part of the question is missing and it says;

Use these parameters: Men's heights are normally distributed with mean 68.6 in. and standard deviation 2.8 in. Women's heights are normally distributed with mean 63.7 in. and standard deviation 2.9 in.

Answer:

A) Percentage of women meeting the height requirement = 72.24%

B) Percentage of men meeting the height requirement = 0.875%

C) Corresponding women's height =67.42 inches while corresponding men's height = 72.19 inches

Step-by-step explanation:

From the question,

For men;

Mean μ = 68.6 in

Standard deviation σ = 2.8 in

For women;

Mean μ = 63.7 in

Standard deviation σ = 2.9 in

Now let's calculate the standardized scores;

The formula is z = (x - μ)/σ

A) For women;

Z = (62 - 63.7)/2.9 = - 0.59

Z = (78 - 63.7)/2.9 = 4.93

The original question cam be framed as;

P(62 < X < 78).

So thus, the probability of only women will take the form of;

P(-0.59 < Z < 4.93) = P(Z<4.93) - P(Z > - 0.59)

From the normal probability table attached, when we interpolate, we'll arrive at P(Z<4.93) = 0.9999996

And P(Z > - 0.59) = 0.277595

Thus;

P(Z<4.93) - P(Z > - 0.59) =0.9999996 - 0.277595 = 0.7224

So, percentage of women meeting the height requirement is 72.24%.

B) For men;

Z = (62 - 68.6)/2.8 = -2.36

Z = (78 - 68.6)/2.8 = 3.36

Thus, the probability of only men will take the form of;

P(-2.36 < Z < 3.36) = P(Z<3.36) - P(Z > - 2.36)

From the normal probability table attached, when we interpolate, we'll arrive at P(Z<3.36) = 0.99961

And P(Z > -2.36) = 0.99086

Thus;

P(Z<3.36) - P(Z > -2.36) 0.99961 - 0.99086 = 0.00875

So, percentage of women meeting the height requirement is 72.24%.

B)For women;

Z = (62 - 63.7)/2.9 = - 0.59

Z = (78 - 63.7)/2.9 = 4.93

The original question cam be framed as;

P(62 < X < 78).

So thus, the probability of only women will take the form of;

P(-0.59 < Z < 4.93) = P(Z<4.93) - P(Z > - 0.59)

From the normal probability table attached, when we interpolate, we'll arrive at P(Z<4.93) = 0.9999996

And P(Z > - 0.59) = 0.277595

Thus;

P(Z<4.93) - P(Z > - 0.59) =0.9999996 - 0.277595 = 0.00875

So, percentage of women meeting the height requirement is 0.875%

C) Since the height requirements are changed to exclude the tallest 10% of men and the shortest10% of women.

For women;

Let's find the z-value with a right-tail of 10%. From the second table i attached ;

invNorm(0.90) = 1.2816

Thus, the corresponding women's height:: x = (1.2816 x 2.9) + 63.7= 67.42 inches

For men;

We have seen that,

invNorm(0.90) = 1.2816

Thus ;

Thus, the corresponding men's height:: x = (1.2816 x 2.8) + 68.6 = 72.19 inches

You might be interested in
NEED ANSWER ASAP . <br> Which table represents a linear function?
alexira [117]

Answer:

Step-by-step explanation:

Answer choice C would be correct since both sides are increasing at a set rate, x is increasing by one while y is increasing by 2 every time. Hope this helps :)

6 0
3 years ago
Please help, brainliest for correct answer
slava [35]

Answer:

The correct answer is m∠2 = 120°

Step-by-step explanation:

There is a triangle rule that states the outer angle of an angle in a triangle is equal to the sum of the remaining two angles in that triangle, which means that m∠2 = 52° + 68° = 120°. This can be proven correct because the sum of two of the angles in the triangle is 120°, which means the final angle is 60°. Since m∠2 is the outer angle of 60°, that means it will be 180° - 60° or 120°.

4 0
3 years ago
Read 2 more answers
Suppose y varies directly as x, and y = 21 when x = 3. Find x when y = 42.
nata0808 [166]

Answer:

x = 24

Step-by-step explanation:

y₂ - y₁

42 - 21 = 21

x + 21

3 + 21 = 24

So when y increases by 21, so does x.

x = 24

7 0
3 years ago
Given |u| = 2.5, |v| = 3.2, and the angle between the vectors is 60°, find the value of u · v?
Alenkasestr [34]

Step-by-step explanation:

u.v=|u||v|cos60°

u.v=(2.5)(3.2)(1/2)

u.v=(8)(1/2)

u.v=4

4 0
3 years ago
Find the distance between the two points in simplest radical form.<br> (-1, -5) and (4,7)
Neporo4naja [7]

Hope t will help u..........

6 0
3 years ago
Other questions:
  • What is the value of x.
    13·2 answers
  • Could someone please answer these ASAP. It is for ratios, rates, proportion &amp; percent. The questions are located in the atta
    13·1 answer
  • Evaluate 6x - y if x=5 and y=8
    8·2 answers
  • Calvin evaluated -2/3 *5 1/6 using the steps below.
    9·1 answer
  • lena's house casts a shadow that is 14 feet long at the same time that lena casts a shaodw that is 3.5 feet long if lena is 4.5
    8·1 answer
  • Please help!! What is the value of the sum? Drag and drop the answer into The box to match the sum with its value. 5/6 + (-1/2).
    6·1 answer
  • Find the volume of the cylinder.<br><br> r = 5 cm<br><br> h = 9 cm
    13·1 answer
  • Hot dogs are sold in packages of 6. Hot dog buns are sold in packages of 8
    6·1 answer
  • ticket sales for a local concert totaled $101,244 yesterday. After the ticket window closed today, the cashiers counted 968 tick
    12·1 answer
  • In Mr. Johanessen's class, 1/4 of the students failed the final exam. Of the remaining students in the class, 1/3 scored an A. W
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!