A set of 50 data values has a mean of 15 and a variance of 25. Find the standard score of a data...

Question

A set of 50 data values has a mean of 15 and a variance of 25. Find the standard score of a data value = 30.

Following are the American College Test (ACT) scores attained by the 25 members of a local high school graduating class:

21	24	23	17	31	19	19	20	19	25	17	23	16
21	20	28	25	25	21	14	19	17	18	28	20

Find P99, P90, and P80 for the ACT scores. [Hint: Use nk/100 to find the location in the ordered data for each percentile.] All work must be show in order to get your assignment graded
2) How is a “discrete” variable different from a “continuous” variable? Please give one example of each, and describe how these examples differ from one another.
Identify what makes flipping a coin and keeping track of tails a binomial experiment .
3) If the random variable z is the standard normal score and a > 0, is it true that P(z < -a) = P(z > a)? Why or why not? Then find the z-score for the standard normal distribution where:
Area₌0.32 in the left tail

005_f9f75k-z4pk3hvj.docx

David · Accepted Answer

2048-11
Sol 1(a):   By using formula,
                       
data value-mean
standard score=,
standard deviation
æö
ç÷
èø
  Given that,
                Data value=30, mean=15, variance=25,
        
Standard deviation=variance,
25
Standard deviation5,
=
=
Now from above formula, put the all values & find the standard score,
        
30-15
standard score=,
5
standard score3,
æö
ç÷
èø
=
Ans: 
standard score3
=
Sol 1(b): First of all put the all number in ascending order. The ascending order is given below,
 
14,16,17,17,17,18,19,19,19,19,20,20,20,2
1,21,21,23,23,24,25,25,25,28,28,31
There are 25 numbers.
P99: Find the number that has  
9925
99% of 2524.75,
100
´
æö
==
ç÷
èø
       Round up to the 25th number in the order, which is equal to
31
,
    So ordered data for percentile P99 is= 
31
P90
: Find the number that has  
9025
90% of 2522.50,
100
´
æö
==
ç÷
èø
       Round up to the 23th number in the order, which is equal to
28
,
    So ordered data for percentile 
P90
 is=
28
P80
: Find the number that has  
8025
80% of 2520,
100
´
æö
==
ç÷
èø
       Take the average of the 20th and 21th number in the order. That is
2525
25,
2
+
æö
=
ç÷
èø
.
    So ordered data for percentile 
P80
is=
25
Sol 2(a): A continuous variable is one that can take any real numerical value. The length of a strip can be anything.

A set of 50 data values has a mean of 15 and a variance of 25. Find the standard score of a data value = 30. Following are the American College Test (ACT) scores attained by the 25 members of a local...

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