2.Children’s heights are normally distributed with a mean of 100 cm and a standard deviation of 6 cm. What proportion of children’s heights is smaller than 94?
To find the proportion of children's heights that is smaller than 94 cm, we need to calculate the z-score and then use a standard normal distribution table.
Step 1: Calculate the z-score
The z-score formula is given by:
z = (x - μ) / σ
Where:
x is the value we are interested in (94 cm in this case)
μ is the mean (100 cm)
σ is the standard deviation (6 cm)
Plugging in the values, we get:
z = (94 - 100) / 6
z = -1
Step 2: Use the standard normal distribution table
The standard normal distribution table provides the proportion of values below a given z-score. In this case, we are interested in finding the proportion below a z-score of -1.
Looking up the z-score of -1 in the standard normal distribution table, we find that it corresponds to a cumulative probability of approximately 0.1587.
Step 3: Interpret the result
The proportion of children's heights that is smaller than 94 cm is approximately 0.1587 or 15.87%.
Therefore, about 15.87% of children's heights are smaller than 94 cm.