Respuesta :
Answer:
a) 0.705015
b) 0.13424
Step-by-step explanation:
We solve using z score formula
z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
The incubation period for the eggs of a house wren is normally distributed with a mean of 336 hours and a standard deviation of 3.5 hours.
a) Find the probability that an egg has an incubation period between 328 and 338 hours.
For x = 328
z = 328 - 336/3.5
z = -2.28571
Probability value from Z-Table:
P(x = 328) = 0.011135
For x = 338
z = 338 - 336/3.5
z = 0.57143
Probability value from Z-Table:
P(x = 338) = 0.71615
The probability that an egg has an incubation period between 328 and 338 hours.
P(x = 338) - (P(x = 328)
0.71615 - 0.011135
= 0.705015
b) Suppose a researcher has fifteen house wren eggs in an incubator. Find the probability that the average incubation time for the fifteen eggs is greater than 337 hours.
We are given a sample of 15 wren eggs,
We use this z score formula
z = (x-μ)/σ/√n, where
x is the raw score
μ is the population mean
σ is the population standard deviation
n is random number of samples
z = 337 - 336/3.5/√15
z = 1.10657
Probability value from Z-Table:
P(x<337) = 0.86576
P(x>337) = 1 - P(x<337) = 0.13424
Suppose it is known that 33% of House wren eggs never hatch. Suppose an ornithologist has forty house wren eggs. Find the probability that less than 25% never hatch.
