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umka21 [38]
3 years ago
14

SAT scores are normally distributed with a mean of 1518 and standard deviation of 325. If 16 SAT scores are randomly selected, f

ind the probability that they have a sample mean that is between 1440 and 1480, P(1440 < sample mean < 1480). Load the leading zero and round your answer to four decimal places.
Mathematics
1 answer:
jonny [76]3 years ago
3 0

Answer:

The probability that a random sample of 16 SAT scores has a sample mean  between 1440 and 1480 is 0.1464

Step-by-step explanation:

The probability that the sample mean is between 1440 and 1480 is equal to the probability that the sample mean is below 1480 minus the probability that the sample mean is below 1440, or

P(1440 < sample mean < 1480)  

=P(sample mean<1480) - P(sample mean<1440)

To find these probabilities we need to calculate the statistic of 1440 and 1480, and it can be calculated as:

t=\frac{X-M}{\frac{s}{\sqrt{N} } } where

  • X is the sample mean (1440,1480)
  • M is the mean SAT scores (1518)
  • s is the standard deviation (325)
  • N is the sample size (16)

then

t(1440)= \frac{1440-1518}{\frac{325}{\sqrt{16} } } =-0.96

t(1480)= \frac{1480-1518}{\frac{325}{\sqrt{16} } } = -0.4677

using the t table with 15 degrees of freedom we can find that

P(sample mean<1480) = P(t<-0.4677) = 0.3225

P(sample mean<1440) = P(t<-0.96) = 0.1761

Then P(1440 < sample mean < 1480)   =0.3225 - 0.1761 = 0.1464

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+

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---------------------------

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1 year ago
How can I use the percent equation???Ex.what number is 40% of 500???and can u solve this one,too.:45 is 25% of what number???THA
HACTEHA [7]
I've been waiting for someone to ask this question.  It's one of my favorite questions to answer.

percent means out of 100 so 1% = 1/100 and 40%=40/100 or 1/25
so for percent of a number, 'of' means multiply so 40% of 500= 40/100 times 500 or 20000/100 or 200



if you multiply a fraction by its recipricol (the number fliped upside down) the you will get 1 so if you multiply 1/2 by 2/1 then you will get 1

thus
percent is out of 100 so 1%=1/100  25%=25/100
if you represent 45 out of something as 45/x then you multiply it by the reciprocal of the fraction that is supposed to be equal (1/2 =2/4) then you will get 1
so 45/x times reciprocal of 100/25 then you will get 1/1 or 4500/25x
so you divide to find x and get 180
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The following is extra
   as stated above 'of' can be taken as multiply so
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3 years ago
Read 2 more answers
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Step-by-step explanation:

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