Answer:
The total length to be calculated = 290.32 days
Step-by-step explanation:
The probability that the total length of pregnancy for 15 randomly selected women is greater than a certain amount is 0.05.
Let the standardized score of this certain amount be z',
P(z>z') = 0.05
But on the normal distribution tables, what we have is P(z≤(any random z-score)
So, expressing P(z>z') in that form,
Mathematically,
P(z>z') = 1 - P(z≤z')
0.05 = 1 - P(z≤z')
P(z≤z') = 1 - 0.05 = 0.95
From the normal distribution table, z' = 1.645
The z-score formula is
z = (x - xbar)/σ
Where z = 1.645
xbar = mean = 264 days
σ = standard deviation = 16 days
x = number of days that corresponds to the z-score of 1.645 = ?
1.645 = (x - 264)/16
x = 26.32 + 264 = 290.32 days.
