Answer :
Final answer:
To find P(x<185), calculate the Z-score for 185 pounds using the mean of 147 and standard deviation of 16 to convert to the standard normal distribution, and then use a Z-table or calculator to find the probability.
Explanation:
To determine P(x<185) for the normal random variable representing the weight of a 40-year-old man with a mean (μ) of 147 pounds and a standard deviation (σ) of 16 pounds, we use the standard normal distribution (Z-distribution). First, calculate the Z-score for the weight of 185 pounds using the formula:
Z = (x - μ) / σ
Substitute the given values:
Z = (185 - 147) / 16
Z = 38 / 16
Z = 2.375
Now, refer to the standard normal distribution table or use a calculator that has the normal distribution function to find P(Z < 2.375). This gives you the probability that a 40-year-old man weighs less than 185 pounds.
