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
Lelechka [254]
3 years ago
12

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 65 inches and standard deviation 4 inch

es. (a) What is the probability that an 18-year-old man selected at random is between 64 and 66 inches tall? (Round your answer to four decimal places.) (b) If a random sample of seven 18-year-old men is selected, what is the probability that the mean height x is between 64 and 66 inches? (Round your answer to four decimal places.) (c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this? The probability in part (b) is much higher because the mean is larger for the x distribution. The probability in part (b) is much higher because the standard deviation is larger for the x distribution. The probability in part (b) is much higher because the mean is smaller for the x distribution. The probability in part (b) is much lower because the standard deviation is smaller for the x distribution. The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
Mathematics
1 answer:
Serhud [2]3 years ago
4 0

Answer:

Step-by-step explanation:

<u>a)</u>

  • Given that ; X ~ N ( µ = 65 , σ = 4 )
  • P ( 64 < X < 66 )

From application of normal distribution ;

  • Z = ( X - µ ) / σ, Z = ( 64 - 65 ) / 4,  Z = -0.25
  • Z = ( 66 - 65 ) / 4,  Z = 0.25

Hence, P ( -0.25 < Z < 0.25 ) = P ( 64 < X < 66 ) = P ( Z < 0.25 ) - P ( Z < -0.25 ) P ( 64 < X < 66 ) = 0.5987 - 0.4013

  • P ( 64 < X < 66 ) = 0.1974

b) X ~ N ( µ = 65 , σ = 4 )

  • P ( 64 < X < 66 )

From normal distribution application ;

  • Z = ( X - µ ) / ( σ / √(n)), plugging in the values,
  • Z = ( 64 - 65 ) / ( 4 / √(12)) = Z = -0.866
  • Z = ( 66 - 65 ) / ( 4 / √(12)) = Z = 0.866

P ( -0.87 < Z < 0.87 )

  • P ( 64 < X < 66 ) = P ( Z < 0.87 ) - P ( Z < -0.87 )
  • P ( 64 < X < 66 ) = 0.8068 - 0.1932
  • P ( 64 < X < 66 ) = 0.6135

c) From the values gotten for (a) and (b), it is indicative that the probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

You might be interested in
A soft-drink machine can be regulated so that it discharges an average of μ oz. per cup. If the ounces of fill are Normally dist
sattari [20]

Answer:

μ = 5.068 oz

Step-by-step explanation:

Normal distribution formula to use the table attached

Z = (x - μ)/σ

where μ is mean, σ is standard deviation, Z is on x-axis and x is a desired point.

98% of 6-oz. cups will not overflow means that the area below the curve is equal to 0.49; note that the curve is symmetrical respect zero, so, 98% of the cases relied between the interval (μ - some value) and (μ + some value)].

From table attached, area = 0.49 when Z = 2.33. From data, σ = 0.4 oz and x = 6 oz (maximum capacity of the cup). Isolating x from the formula gives

Z = (x - μ)/σ

2.33 = (6 - μ)/0.4

μ = 6 - 2.33*0.4

μ = 5.068

This means that with a mean of 5 oz and a standard deviation of 0.4 oz, the machine will discharge a maximum of 6 oz in the 98% of the cases.

4 0
3 years ago
Solve 3x + 5 ⩾ x + 17
Ugo [173]

Answer:

Step-by-step explanation:

Simplifying

3x + 5 = x + 17

Reorder the terms:

5 + 3x = x + 17

Reorder the terms:

5 + 3x = 17 + x

Solving

5 + 3x = 17 + x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.

5 + 3x + -1x = 17 + x + -1x

Combine like terms: 3x + -1x = 2x

5 + 2x = 17 + x + -1x

Combine like terms: x + -1x = 0

5 + 2x = 17 + 0

5 + 2x = 17

Add '-5' to each side of the equation.

5 + -5 + 2x = 17 + -5

Combine like terms: 5 + -5 = 0

0 + 2x = 17 + -5

2x = 17 + -5

Combine like terms: 17 + -5 = 12

2x = 12

Divide each side by '2'.

x = 6

Simplifying

x = 6

5 0
3 years ago
Applying GCF and LCM to fraction Operations?<br>.<br>. PLZ HELP
I am Lyosha [343]
When multiplying fractions just multiply the numerator and denominators together, then simplify the fraction you get.

To solve the addition problem, first convert 2 and 1/2 to an improper fraction. It should be 5/2. Now 3/8 and 5/2 must be added together.

To add these, they must have the same denominator. Let's give 5/2 a denominator of 8, so it matches 3/8.

To give 5/2 a denominator of 8, you are starting with a denominator of 2. 2 × 4 = 8, so you must multiply 5/2 by 4.

You should get 20/8. Now you have to add 20/8 and 3/8. The only thing you add is the numerator, so you should get 23/8 as a final answer.

For the subtraction problem, do these same steps to make the fractions you must subtract have the same denominator, then subtract only the numerator to get the answer. Once you solve the subtraction problem, text me what you got so I can check it for you. :)
4 0
3 years ago
Help me with this pls
zhannawk [14.2K]

Answer: The answer is 3

Step-by-step explanation:

To find the slope u turn it into a shape it could make such as in this case u are able to make a box like this. For such as u can use this picture to get a better understand but hope this helps :)

6 0
2 years ago
Yea I am lost help me
IgorLugansk [536]

Answer:

I'm not sure bu I think the answer is 8 × x × 7 = 2

4 0
2 years ago
Read 2 more answers
Other questions:
  • Which of the following is NOT a typical tennis competition (connexus)
    8·2 answers
  • What are the solutions to the equation (x – 6)(x + 8) = 0?
    5·2 answers
  • Suppose a parabola has an axis of symmetry at x=-1 a maximum height of 6 and passes through point -2,1. Write the equation of th
    9·1 answer
  • the height of an airplane as it descends to an airport runway is it rational ,integers, whole ,or irrational?
    13·1 answer
  • Tim can mow 4 lawns in 6 hours. How many lawn(s) can he mow in 1 hour?
    15·2 answers
  • Can someone please tell me the aswer​
    11·1 answer
  • Which linear inequality is represented by the graph?
    11·2 answers
  • The function p(h)=0.375h+3 represents the supply model to determine the millions of
    7·1 answer
  • Help me pls plz please teachers math simple math lol ok smart wow cool points brainly tiktok
    12·1 answer
  • What is a surface area of the cuboid with 4,5 and 9
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!