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
Find the surface area of the square pyramid 8mm 6mm
bija089 [108]

Answer:

136 mm²

Step-by-step explanation:

A=a^{2} +2a\sqrt{\frac{a^{2} }{4} } +h^{2}

A=6^{2} +2(6)\sqrt{\frac{6^{2} }{4} } +8^{2}

A=36 +12\sqrt{\frac{36 }{4} } +64

A=36 +12\sqrt{9 } +64

A=36 +12(3)+64

A=36 +36+64

A = 136

5 0
3 years ago
You buy a storage case that holds 170 collectible die-cast cars. You have 137 die-cast cars. Write an inequality that describes
Murljashka [212]

Answer:

137 + x <= 170

Step-by-step explanation:

The following inequality will describe this scenario.

137 + x <= 170

the variable x in this scenario represents the total number of cars that you will purchase. This number is added to the number of toy cars that you already own which is 137. As long as this sum is less than or equal to 170 then your storage case will hold them.

4 0
3 years ago
Which statement is true regarding the dilation ?
frez [133]
The dilation is a reduction because n > 1

Hope this helps :)
3 0
3 years ago
In a fitness club, the ratio of male and female is 3:2. Base on their ability level, they are group into 3 different groups, A,B
ArbitrLikvidat [17]

Answer:35, 1

Step-by-step explanation:

8 0
3 years ago
3/30 = n/50<br><br> n = (Blank)<br><br> Find n.
UNO [17]
<span>3/30 = n/50
</span><span>1/10 = n/50
10n = 50
n = 50/10
n=5</span>
3 0
3 years ago
Other questions:
  • What’s 27 x 89 + 372 x 17192728282
    9·1 answer
  • $0.26/hour=$_____/day
    10·2 answers
  • Which of the following is not a reason young drivers have higher auto insurance premiums than older drivers
    5·2 answers
  • Si el gerente de control de calidad desea estimar la media de vida de lámparas con 20 horas, con un nivel de confianza del 95% y
    5·1 answer
  • If you earn $3250 per month and you expect your earnings to increase by 2.2% per year, how much do you think you will be making
    6·1 answer
  • IM GIVING 100 POINTS AND BRAINLIEST JUST VERIFY ALL THESE QUESTIONS ARE CORRECT IF THEY'RE NOT CORRECT TELL ME, PLEASE AND THANK
    15·2 answers
  • Pls help find the sum thank you
    5·2 answers
  • Can someone please help me I will give you brainleist but please don’t put no links
    6·1 answer
  • Help me PLEASEEEEEEEEEEEEE
    12·1 answer
  • Which matrix represents the vertices of the rectangle after it is scaled by a factor of 3?.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!