a rocket club makes its own rockets. The rockets go to a mean height of 1100 feet with a standard deviation of 60 feet. if the club fires 36 rockets, what is probability that the mean heights of the rockets will be greater than 1080p feet
Z = (score-mean)/SEm
SEm = SD/√n
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.
You will use probability between score and mean plus 50%.
36.0144
To find the probability that the mean heights of the rockets will be greater than 1080 feet, we can use the z-score formula and the central limit theorem.
1. Calculate the z-score: The z-score is a measure of how many standard deviations an observation or data point is from the mean. The formula for the z-score is:
z = (x - μ) / (σ / √n)
Where:
- x is the value in question (1080 feet in this case)
- μ is the mean height of the rockets (1100 feet)
- σ is the standard deviation (60 feet)
- n is the sample size (36 rockets)
Plugging in the values:
z = (1080 - 1100) / (60 / √36)
= -20 / (60 / 6)
= -20 / 10
= -2
2. Look up the z-score in the standard normal distribution table (also known as the z-table) or use a calculator that can calculate the corresponding area under the normal curve. The z-table provides the probability of finding a value to the left of the given z-score.
The z-table value for -2 is approximately 0.0228. However, since we want the probability of the mean heights being greater than 1080 feet, we need to find the area to the right of the z-score.
P(z > -2) = 1 - P(z ≤ -2)
= 1 - 0.0228
= 0.9772
3. Convert the probability to a percentage.
The probability that the mean heights of the rockets will be greater than 1080 feet is 0.9772, which is equivalent to 97.72%.
Therefore, the probability is approximately 97.72% that the mean heights of the rockets will be greater than 1080 feet.