A battery manufacturer claims that the lifetime of a certain type of battery has a population mean of 40 hours and a standard deviation of 5 hours. Let X represent the mean lifetime of the batteries in a simple random sample of size 100.

If the claim is true, what is P(X(bar) < 36.7)?

Whenever I work out the problem I keep getting a P that's much too large to be correct. A step in the right direction would be very much appreciated!

The probability is found to be 0.2546.

Step-by-step explanation:

This is the case of normal distribution. The data given is:

Mean = μ = 40 hours

Standard Deviation = σ = 5 hours

X = 36.7 hours

Therefore, from the formula of normal distribution, we calculate Z, firt. The formula is as follows:

Z = (X - μ)/σ

Z = (36.7 - 40)/5

Z = -0.66

Therefore,

P (X < 36.7) = P (Z < -0.66)

Hence, from the table attached, we find the probability of z < -0.66, through normal distribution graph.

P (X < 36.7) = 0.2546

honestly bro aint no one got time to answer these dumb question just do it p***y

step-by-step explanation:

i need a diagram

step-by-step explanation:

no