Given Information:
Mean clear height = μ = 22 feet
Standard deviation of clear height = σ = 4 feet
Required Information:
a) P(X > 16) = ?
b) P(X < 14) = ?
c) P(25 < X < 30) = ?
Answer:
a) P(X > 16) = 93.12%
b) P(X < 14) = 2.27%
c) P(25 < X < 30) = 20.39%
Step-by-step explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
a) We want to find out the probability that the clear height is greater than 16 feet.
The z-score corresponding to -1.5 is 0.0668
Therefore, the probability that the clear height is greater than 16 feet is 93.12%
b) We want to find out the probability that the clear height is less than 14 feet
The z-score corresponding to -2 is 0.02275
Therefore, the probability that the clear height is less than 14 feet is 2.27%
c) We want to find out the probability that the clear height is between 25 and 30 feet.
The z-score corresponding to 0.75 is 0.7734 and 2 is 0.9773
Therefore, the probability that a child spends more than 4 hours and less than 8 hours per day unsupervised is 20.39%
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.5, 2.2, 0.5 etc.)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 1.50 then go for 0.00 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.