in a standard normal distribution, what percentage of observations lie above z = 1.65? find the z - table…
in a standard normal distribution, what percentage of observations lie above z = 1.65? find the z - table here. 4.95% 5.48% 6.06% 95.05%
Answer
Explanation:
Step1: Understand the z - table
The z - table gives the cumulative probability $P(Z\leq z)$. For a standard normal distribution, the total area under the curve is 1.
Step2: Look up the value in the z - table
Looking up $z = 1.65$ in the standard normal z - table, we find that $P(Z\leq1.65)=0.9505$.
Step3: Calculate the probability above z = 1.65
We know that $P(Z > 1.65)=1 - P(Z\leq1.65)$. Substituting the value from the z - table, we get $P(Z > 1.65)=1 - 0.9505 = 0.0495$.
Step4: Convert to percentage
To convert the probability to a percentage, we multiply by 100. So $0.0495\times100 = 4.95%$.
Answer:
4.95%