Answer:
a) 0.4164
Step-by-step explanation:
Mean lifespan (μ) = 18.8 days
Standard deviation (σ) = 2 days
For any given lifespan 'X', the z-score is:
For X=12.04 days:
A z-score of -3.38 falls in the 0.036-th percentile of a normal distribution.
For X=18.38 days:
A z-score of -3.38 falls in the 41.68th percentile of a normal distribution.
The probability that a butterfly lives between 12.04 and 18.38 days is
Answer:
About 9.4 units
Step-by-step explanation:
Answer:
0.8413 = 84.13% probability that a bolt has a length greater than 2.96 cm.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 3 cm and a standard deviation of 0.04 cm.
This means that
What is the probability that a bolt has a length greater than 2.96 cm?
This is 1 subtracted by the p-value of Z when X = 2.96. So
has a p-value of 0.1587.
1 - 0.1587 = 0.8413
0.8413 = 84.13% probability that a bolt has a length greater than 2.96 cm.