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
DIA [1.3K]
3 years ago
8

A selective university advertises that 96% of its bachelor’s degree graduates have, on graduation day, a professional job offer

or acceptance in a graduate degree program in their major area of study. In a sample of 227 recent graduates this was true of 209 of them. The probability of obtaining a sample proportion as low as or lower than this, if the university’s claim is true, is about:________
a. 0.015
b. 0.001
c. 0.131
d, 0.084
Mathematics
1 answer:
OLEGan [10]3 years ago
6 0

Answer:

The probability is  P( p <  0.9207) = 0.0012556

Step-by-step explanation:

From the question we are told

  The population proportion is p = 0.96

 The sample size is  n  =  227

 The number of graduate who had job is  k = 209

Generally given that the sample size is large enough  (i.e n >  30) then the mean of this sampling distribution is  

       \mu_x = p = 0.96

Generally the standard deviation of this sampling distribution is  

    \sigma  = \sqrt{\frac{p (1 - p )}{n} }

=>  \sigma  = \sqrt{\frac{0.96 (1 - 0.96 )}{227} }

=>  \sigma  = 0.0130

Generally the sample proportion is mathematically represented as

      \^ p =  \frac{k}{n}

=> \^ p =  \frac{209}{227}

=> \^ p =  0.9207

Generally probability of obtaining a sample proportion as low as or lower than this, if the university’s claim is true, is mathematically represented as

     P( p <  0.9207) = P( \frac{\^ p - p }{\sigma } <  \frac{0.9207 - 0.96}{0.0130 }  )

\frac{\^ p - p}{\sigma }  =  Z (The  \ standardized \  value\  of  \ \^ p )

   P( p <  0.9207) = P(Z< -3.022 )

From the z table  the area under the normal curve to the left corresponding to    -3.022  is

     P(Z< -3.022 ) = 0.0012556

=> P( p <  0.9207) = 0.0012556

You might be interested in
Can somebody plz help on this homework?
exis [7]
Basically, if the words in the word bank are similar or opposing or cause and effect add them to the bank
3 0
3 years ago
FIRST ONE TO ANSWER WINS BRAINLIEST (ANSWER THE RED) PLS
Troyanec [42]

Answer:

Ok so Preston has 0.5 hags of mulch for each square yard on the first one and the second one is 1 yard per

Step-by-step explanation:


8 0
3 years ago
Pls help! The price of an item has dropped to
murzikaleks [220]
The percentage decrease is 60% decrease because it changed by 81 and 81 is 60% of 135
4 0
2 years ago
Heights for women are bell-shaped with a mean of 65 inches and standard deviation of 2.5 inches. If a random sample of 16 women
loris [4]

Answer:

μ= 65 inches; σ= 0.625 inch

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed(bell-shaped) random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\mu = 65, \sigma = 2.5

By the central limit theorem, the sample of 16 will have:

\mu = 65, \sigma = \frac{2.5}{\sqrt{16}} = 0.625

So the correct answer is:

μ= 65 inches; σ= 0.625 inch

8 0
2 years ago
Need to know the area of the composite figure.
Deffense [45]

Answer:

  51 m^2

Step-by-step explanation:

The shaded area is the difference between the area of the overall figure and that of the rectangular cutout.

The applicable formulas are ...

  area of a triangle:

     A = (1/2)bh

  area of a rectangle:

     A = bh

  area of a trapezoid:

     A = (1/2)(b1 +b2)h

___

We note that the area of a triangle depends only on the length of its base and its height. The actual shape does not matter. Thus, we can shift the peak of the triangular portion of the shape (that portion above the top horizontal line) so that it lines up with one vertical side or the other of the figure. That makes the overall shape a trapezoid with bases 16 m and 10 m. The area of that trapezoid is then ...

  A = (1/2)(16 m + 10 m)(5 m) = 65 m^2

The area of the white internal rectangle is ...

  A = (2 m)(7 m) = 14 m^2

So, the shaded area is the difference:

  65 m^2 -14 m^2 = 51 m^2 . . . . shaded area of the composite figure

_____

<em>Alternate approach</em>

Of course, you can also figure the area by adding the area of the triangular "roof" to the area of the larger rectangle, then subtracting the area of the smaller rectangle. Using the above formulas, that approach gives ...

  (1/2)(5 m)(16 m - 10 m) + (5 m)(10 m) - (2 m)(7 m) = 15 m^2 + 50 m^2 -14 m^2

  = 51 m^2

7 0
3 years ago
Other questions:
  • To raise funds, a school sells two kinds of raffle tickets, Adults pay $6, children pay $1.50. Sales for both amounted to $900.
    13·1 answer
  • Write the equation in slope-intercept form 3× + y =9​
    11·1 answer
  • Find the sum (1−5q)+2(2.5q+8) =
    14·2 answers
  • Mary has 3 rolls of wallpaper. Each roll can cover 127.8 sq ft. If Mary uses all 3 rolls of wallpaper how much sq ft would it co
    6·1 answer
  • Why are job security, credit history, and debt-to-income ratio so important to lenders when considering people for loans?
    12·1 answer
  • What is an expression
    14·1 answer
  • Curtis decided to go on a road trip to Canada. On the first day of his trip, he drove for 13 hours and traveled 884 miles. At wh
    5·2 answers
  • frank liked to buy packs of baseball cards. on 3 different days, he bought 3 packs. on 3 other days, he bought 4 packs each day.
    11·1 answer
  • Help me please i need some help.
    7·2 answers
  • Simplify the expression.<br><br> 5(x-1)
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!