Find the value of: such that 0.9722 of the area les between-z and: Round your an

Question

Find the value of: such that 0.9722 of the area les between-z and: Round your answer to two decimal places Answer 2 Points Keypad If you would like to look up the value in a table, sellect the table you want to view, then either click the cell at the intersection of the row and column or use the arrow keys to find the appropriate cell in the table and select it using the Space key. Note Selecting a cel will return he value associaned wih the column and row headers for that cell Normal Table 0 to : Normal Table- Normal Tableto Next

Explanation / Answer

the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 0
standard Deviation ( sd )= 1
LOWER/BELOW
P ( Z < x ) = 0.0139
Value of z to the cumulative probability of 0.0139 from normal table is -2.200097
P( x-u/s.d < x - 0/1 ) = 0.0139
That is, ( x - 0/1 ) = -2.200097
--> x = -2.200097 * 1 + 0 = -2.200097 ~ -2.2

UPPER/TOP
P ( Z > x ) = 0.0139
Value of z to the cumulative probability of 0.0139 from normal table is 2.200097
P( x-u / (s.d) > x - 0/1) = 0.0139
That is, ( x - 0/1) = 2.200097
--> x = 2.200097 * 1+0 = 2.200097 ~ 2.2

To find P(a < = Z < = b) = F(b) - F(a),
P(-2.2 < X < 2.2) = 0.9722

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