The amount of meat on a Subbies foot-long sub follows a Normal distribution, with a mean of 8 ounces and a standard deviation of
0.6 ounce. A random sample of 25 subs is selected every day and measured. What is the probability that the mean weight will exceed 8.2 ounces?
1 answer:
Answer:
95.15%
Step-by-step explanation:
We have that the mean (m) is equal to 8, the standard deviation (sd) 0.6 and the sample size (n) = 25
They ask us for P (x <8.2)
For this, the first thing is to calculate z, which is given by the following equation:
z = (x - m) / (sd / (n ^ 1/2))
We have all these values, replacing we have:
z = (8.2 - 8) / (0.6 / (25 ^ 1/2))
z = 1.66
With the normal distribution table (attached), we have that at that value, the probability is:
P (z <1.66) = 0.9515
It means that the probability that it exceeds 8.2 ounces is 95.15%
You might be interested in
Answer:
[34,54]
Step-by-step explanation:
-The empirical rule states that the 95% of the sampled observations will fall within two standard deviations of the mean for a normally distributed population.
Where:
- 68% is the first standard deviation
- 95% is the second standard deviation about the mean
- 99.7% is the 3rd standard deviation about the mean.
-Therefore. the middle 95% interval is calculated as:
Hence, the interval is [34,54]