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
Katarina [22]
2 years ago
14

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.2.a. If the distri

bution is normal, what is the probability that the sample mean hardness for a random sample of 9 pins is at least 51?b. Without assuming population normality, what is the (approximate) probability that the sample mean hardness for a random sample of 40 pins is at least 51?
Mathematics
1 answer:
zalisa [80]2 years ago
5 0

Answer:

a

 P(\= X \ge 51 ) =0.0062

b

P(\= X \ge 51 ) = 0

Step-by-step explanation:

From the question we are told that

The mean value is \mu = 50

The standard deviation is  \sigma = 1.2

Considering question a

The sample size is  n = 9

Generally the standard error of the mean is mathematically represented as

      \sigma_x = \frac{\sigma }{\sqrt{n} }

=>   \sigma_x = \frac{ 1.2 }{\sqrt{9} }

=>  \sigma_x = 0.4

Generally the probability that the sample mean hardness for a random sample of 9 pins is at least 51 is mathematically represented as

      P(\= X \ge 51 ) = P( \frac{\= X - \mu }{\sigma_{x}}  \ge \frac{51 - 50 }{0.4 } )

\frac{\= X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ \= X )

     P(\= X \ge 51 ) = P( Z  \ge 2.5 )

=>   P(\= X \ge 51 ) =1-  P( Z  < 2.5 )

From the z table  the area under the normal curve to the left corresponding to  2.5  is

    P( Z  < 2.5 ) = 0.99379

=> P(\= X \ge 51 ) =1-0.99379

=> P(\= X \ge 51 ) =0.0062

Considering question b

The sample size is  n = 40

   Generally the standard error of the mean is mathematically represented as

      \sigma_x = \frac{\sigma }{\sqrt{n} }

=>   \sigma_x = \frac{ 1.2 }{\sqrt{40} }

=>  \sigma_x = 0.1897

Generally the (approximate) probability that the sample mean hardness for a random sample of 40 pins is at least 51 is mathematically represented as  

       P(\= X \ge 51 ) = P( \frac{\= X - \mu }{\sigma_x}  \ge \frac{51 - 50 }{0.1897 } )

=> P(\= X \ge 51 ) = P(Z  \ge 5.2715  )

=>  P(\= X \ge 51 ) = 1- P(Z < 5.2715  )

From the z table  the area under the normal curve to the left corresponding to  5.2715 and

=>  P(Z < 5.2715  ) = 1

So

   P(\= X \ge 51 ) = 1- 1

=> P(\= X \ge 51 ) = 0

You might be interested in
One marketing company assumes a yearly growth in social media followers of 2.5% after implementing their ideas. Their client cur
tatyana61 [14]

Answer:

The number of follower after x years is  40,000(1.025)^{x}

Step-by-step explanation:

Given as :

The number of current followers = p = 40,000

The rate of growth of follower = r = 2.5%

The time period of growth = t = x years

Let The number of follower after x years = A

<u />

<u>Now, According to question</u>

The number of follower after x years = number of current followers × (1+\dfrac{\textrm rate}{100})^{\textrm time}

Or, A = p × (1+\dfrac{\textrm r}{100})^{\textrm t}

Or, A = 40,000 × (1+\dfrac{\textrm 2.5}{100})^{\textrm x}

Or, A = 40,000 × (1.025)^{x}

So, The number of follower after x years = A = 40,000 × (1.025)^{x}

Hence, The number of follower after x years is  40,000(1.025)^{x}  Answer

4 0
3 years ago
You buy 70 of your favorite songs from a Web site that charges ​$0.98 for each song. What is the cost of 70 ​songs? Use mental m
Leya [2.2K]

Answer: If this isn't a trick question it is $68.60

Step-by-step explanation: You just multiply the 98 cents by the 70 songs.

7 0
2 years ago
Read 2 more answers
What is the factored form of 8x^24-27^6
gladu [14]
The answer is x^6(2X^6-3)(4X^12+6X^6+9)
8 0
2 years ago
Hi y’all can plz help me with this it would mean a lot.....Thanks!
pantera1 [17]

Answer:

where's the question 0.0

3 0
2 years ago
Which represents the solution(s) of the system of equations, y = x2 – 2x – 15 and y = 8x – 40? Determine the solution set algebr
almond37 [142]

Answer:

(5, 0 )

Step-by-step explanation:

Given the 2 equations

y = x² - 2x - 15 → (1)

y = 8x - 40 → (2)

Substitute y = x² - 2x - 15 into (2)

x² - 2x - 15 = 8x - 40 ( subtract 8x - 40 from both sides )

x² - 10x + 25 = 0 ← in standard form

(x - 5)² = 0 ← in factored form, thus

x - 5 = 0 ⇒ x = 5

Substitute x = 5 into (2) for corresponding value of y

y = 8(5) - 40 = 40 - 40 = 0

Solution is (5, 0 )

3 0
3 years ago
Other questions:
  • How is twelve divided by fifteen equal to eight.
    14·1 answer
  • Ms. Albero decided to make juice to serve along with the pizza at the Student Government party. The directions said to mix 2 sco
    6·2 answers
  • Find the area to the combined rectangle
    12·1 answer
  • Which of the equations below could be the equation of this parabola?
    5·2 answers
  • At the zoo the polar bears are fed from 4 kg bucket of a fish day.If each bears eats 3 upon 5 from that bucket what amount of fi
    15·1 answer
  • Picture attached multiple choice :3
    10·1 answer
  • Graphing standard form inequalities help plz
    10·1 answer
  • Which of the Following is an example of a claim?
    10·1 answer
  • A total of 42 gallons of a glycol solution needs to be added to a heating water loop to ensure the water does not freeze if ther
    13·1 answer
  • Find the equation of the straight line with the following gradient point c) 5, (-1,-3)​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!