The weights of steers in a herd are distributed normally. The standard deviation is 200 lbs and the mean steer weight is 1200 lbs. Find the probability that the weight of a randomly selected steer is less than 1560 lbs. (Round your answer to 4 places).
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
To find the probability that the weight of a randomly selected steer is less than 1560 lbs, we need to calculate the z-score and find the corresponding probability using the standard normal distribution.
The z-score is given by the formula:
z = (x - μ) / σ
where x is the value we want to find the probability for (1560 lbs), μ is the mean steer weight (1200 lbs), and σ is the standard deviation (200 lbs).
Plugging in the values, we get:
z = (1560 - 1200) / 200
z = 360 / 200
z = 1.8
Now, we need to find the cumulative probability up to z = 1.8 using a standard normal distribution table or a calculator.
Looking up the z-score of 1.8 in the table, we find that the corresponding cumulative probability is approximately 0.9641.
Therefore, the probability that the weight of a randomly selected steer is less than 1560 lbs is approximately 0.9641 (rounded to 4 decimal places).
To find the probability that the weight of a randomly selected steer is less than 1560 lbs, we can use the standard normal distribution.
Step 1: Standardize the value
To do this, we need to calculate the z-score of 1560 lbs using the formula:
z = (x - μ) / σ
where x is the value we want to standardize, μ is the mean steer weight, and σ is the standard deviation.
z = (1560 - 1200) / 200
z = 360 / 200
z = 1.8
Step 2: Find the probability using a Z-table or calculator
Once we have the z-score, we can look up the corresponding probability in a standard normal distribution table (also called a Z-table). The Z-table gives us the probability of a standard normal random variable being less than a given z-score.
Using the Z-table, we find that the probability corresponding to a z-score of 1.8 is 0.9641.
Step 3: Round the answer
Finally, round the probability to 4 decimal places.
The probability that the weight of a randomly selected steer is less than 1560 lbs is approximately 0.9641.