Question

If x' is a normal variate, then the area
to the left of Z=1.78 is
a) o. 5 b) 0.96 25
d)0.087
c. 1​

Answer 1

Answer:

option C is the correct answer

Step-by-step explanation:

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Answer 2

Given is a normal variate 'x', Find the area to the left of $z=1.78$.

Explanation:

• The graph of a normal distribution is symmetric about its mean.
• The total area under a normal distribution curve is always one.
• Hence, the area under the normal curve on each side of the mean is equal due to symmetry and is equal to $0.5$.
• Now for the area on the left side of $z=1.78$ we get $z\leq 1.78$
• $A=ar(z\leq 0)+ar(0\leq z\leq 1.78)\\A=0.5+ar(0\leq z\leq 1.78)$  
• Now the required area under the curve for z between $0-1.78$ we refer to the standard normal table.
• In the table, the value corresponding to $1.7$ in first vertical column and $0.08$ in the first horizontal row is the area required.
• From the table we get, $ar(0\leq z\leq 1.78)= 0.4625$
• The final area is,      
• $A=0.5+0.4625\\A=0.9625$       -----Answer is option(b)