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
What is the simplified answer to this problem 12 &gt; -3x + 6
Verdich [7]

In this question, you're simplifying the inequality by solving for x.

Solve for x:

12 > -3x + 6

<em>flip the equation:</em>

-3x + 6 < 12

<em>subtract 6 from both sides</em>

-3x < 6

<em>divide both sides by -3, while also flipping the inequality</em>

x > -2

Answer:

x > -2

8 0
3 years ago
A soup recipe requires 40 fluid ounces of water. How many pints of
NARA [144]

Answer:

US Pints: 2.5, Imperial Pints: ~2.1 (If you live in the US, do 2.5, but if not, then do ~2.1.)

Step-by-step explanation:

To do this, we need to convert fluid ounces to US pints. To do this, you divide the amount of fluid ounces by 16. When we divide 40 by 16, we get 2.5. This means that the soup needs 2.5 pints of water. If you are talking about imperial pints, then we divide the amount of fluid ounces by 19.215. This gets us 2.08, which we can round to 2.1. If you live in the US, do 2.5, but if not, then do ~2.1. I hope this helps!

8 0
2 years ago
A book has 8 chapters of equal length. Mary has read 4 chapters. What fraction of the book does Mary have left to read
11111nata11111 [884]

Answer:  1/2 I am almost sure thesis the right answer

7 0
2 years ago
Read 2 more answers
What equation does the model represent?
Vesnalui [34]

It would be 62+23=94 because you'll need to add the tens and the ones, then add it up

I think-_-


7 0
3 years ago
Can 121/12 be simplified to be smaller than it already is?
mr_godi [17]

Answer:

no

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • Determine the type and degree of each of the following polynomial expressions
    9·1 answer
  • -27 = 3 (x - 2) How do I solve this? Step by step please
    5·1 answer
  • You put $939 into an investment at 8% for six years. What will the balance be at the end of six years?
    14·2 answers
  • Please help right now please
    11·1 answer
  • A food truck owner randomly samples 100 customers on two separate days to see what food items they bought. The data shows the re
    9·2 answers
  • Last week Jean ran 2 fewer than 4m miles. This week she ran 0.5 miles more than last week. Write and simplify an expression for
    6·1 answer
  • Sketch the graph of the inequality<br> y-3x&gt;-2
    14·1 answer
  • Please help pleaseeee
    7·2 answers
  • What is the slope of the line whose equation is -48 = 2x - 8y?<br> Enter your answer in the box.
    5·1 answer
  • A line passes through the points (7, 8) and (–7, 10). What is its equation in slope-intercept form?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!