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

a function could be identified in 3 ways either on a chart,graph, or ordered pairs. first a function is that each point has its own. the rule is that there can be many x's to one y but there can not be 2 x's at different y's. so on a graph when you put a straight line through the y's there should be one dot only to be a function.

step-by-step explanation:

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step-by-step explanation: