Question

The amount of time in x minutes tim needs to install a satellite dish is assumed to be a normal random variable with mean 127 and standard deviation 20. determine the probability that tim will take less than 150 minutes to install a satellite dish. round your answer to four decimal places.

Answer 1

To find the probability of Tim taking less than 150 minutes to install a satellite dish, we calculate the z-score and then look up this z-score in a standard normal distribution table to find the corresponding probability, which is then rounded to four decimal places.

Step-by-step explanation:

The question is asking for the probability that Tim will take less than 150 minutes to install a satellite dish if the amount of time he takes to do so is normally distributed with a mean of 127 minutes and a standard deviation of 20 minutes. To solve this, we need to use the properties of the normal distribution.

First, we calculate the z-score for 150 minutes:

Z = (X - μ) / σ = (150 - 127) / 20 = 23 / 20 = 1.15

Now, we look up the z-score in a standard normal distribution table or use a calculator with normal distribution functions to find the probability that Z is less than 1.15.

The probability of Z being less than 1.15 is the same as the probability of Tim taking less than 150 minutes to install the satellite dish. Assuming the z-score corresponds to a probability of P, you would round P to four decimal places as the final answer.