The giant pandas at the zoo consume approximately 30 pounds of bamboo each day. If you were to collect data on the amount of bam
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Answer:
85.31% probability that their mean rebuild time exceeds 8.1 hours.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.1 hours.
This is 1 subtracted by the pvalue of Z when X = 8.1. So
By the Central Limit Theorem
has a pvalue of 0.1469
1 - 0.1469 = 0.8531
85.31% probability that their mean rebuild time exceeds 8.1 hours.
Given:
The growth of a sample of bacteria can be modeled by the function
where, b is the number of bacteria and t is time in hours.
To find:
The number of total bacteria after 3 hours.
Solution:
We have,
where, b is the number of bacteria and t is time in hours.
Substituting t=3, we get the number of total bacteria after 3 hours.
Number of bacteria cannot be decimal value. So, approximate the value to the nearest whole number.
Therefore, the number of total bacteria after 3 hours is about 3003.