The question is not written correctly
Complete Question
The mean speed of vehicles on a stretch of I-84 is 69.5 mph, with a standard deviation of 4 mph. A random sample of 64 vehicles is selected. Find the probabilty that the mean speed is 70 mph
Answer:
0.84134
Explanation:
When given a random number of samples when asked to find probability of that a mean is equal to, less than or greater than a given number, the z score formula we use is :
z = (x- μ)/Standard error, where
x is the raw score,
μ is the population mean
n = Random number of samples
Standard error = is the population standard deviation/square root of randy number of samples
= σ /√n
Standard error = σ /√n
σ = 4 mph, n = 64
= 4/√64
= 4/8 = 1/2
= 0.5
z = (x- μ)/Standard error
x = 69.5mph μ = 70mph ,Standard error = 0.5
z = 70 - 69.5/0.5
z = 1
Using the z score table for find the probability,
P(x = 70) = P(z = 1)
= 0.84134
Therefore, the probability that the mean is 70mph = 0.84134