Final answer:
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.