Cause the question on the second paper is not very clear so

Cause the question on the second paper is not very clear, so I write a new one showing on the first picture.

Solution

The data is,

{4 3 7 10 8 4 4 2 10 6}

Percentiles which divides data into 100 equal parts.

Deciles which divides data into 10 equal parts.

First arrange data in ascending order.

EXCEL syntax for finding percentiles and deciles is,

P37 :

=PERCENTILE(array, k)

arrray is select arranged data.

k = 37/100 = 0.37

P90 :

=PERCENTILE(array, k)

arrray is select arranged data.

k = 90/100 = 0.9

P37 = 4

P90 = 10

D8 :

For decile EXCEL syntax is,

=PERCENTILE(array, k)

arrray is select arranged data.

k = 8/10= 0.8

D8 = 8.4

Find P(1.11 < Z < 1.94) :

P(1.11 < Z < 1.94) = P(Z < 1.94) - P(Z < 1.11)

EXCEL syntax for findind probability is,

=NORMSDIST(z)

where z is 1.94

P(Z < 1.94) = 0.9738 (EXCEL always gives left tail probability)

again use syntax for z is 1.11.

P(Z < 1.11) = 0.8665

P(1.11 < Z < 1.94) = 0.9738 - 0.8665 = 0.1073

P(Z < -0.36) :

EXCEL syntax :

=NORMSDIST(z)

where z is -0.36

P(Z < -0.36) = 0.3594

P(-0.62 < Z < 1.06) = P(Z < 1.06) - P(Z < -0.62)

P(-0.62 < Z < 1.06) = 0.8554 - 0.2676

P(-0.62 < Z < 1.06) = 0.5878

X is normal with mu = 50 and sd = 8 :

Z-value for x=62:

We can\'t find exact probability in continous distribution therefore we make here continuity correction.

62 - 0.5 < x < 62 + 0.5

61.5 < x < 62.5

Now we can find z-score for these two values.

z = (x - mu) / sd

(61.5 - 50) / 8 < (x - mu)/sd < (62.5 - 50) / 8

1.4375 < Z < 1.5625

P(X > 40) = 1 - P(X <=40)

z-score for x = 40 is,

z = (40 - 50) / 8 = -1.25

P(Z > -1.25) = 1 - P(Z < -1.25)

By using EXCEL we can find P(Z < -1.25).

syntax is,

=NORMSDIST(z)

where z is -1.25

P(Z > -1.25) = 1 - 0.1056 = 0.8944

True and False :

1) True

2) True

3) False because m=30 and 30 is even number.

Median formula is,

Median = [ (m/2)th observation + (m/2 + 1)th observation ] / 2

Median =( 15th observation + 16th observation ) / 2

4) True

5) True

6) True