Is it possible for a logarithm to equal to a negative number
1 answer:
You might be interested in
Alice should pick the enlarged-photo with dimensions of 8-inch by 10-inch.
Step-by-step explanation:
Step 1:
In order for a part of the photo to not be cut off, the enlarged photo's dimensions should be of a constant ratio with the original photo's dimensions.
We divide the dimensions of the enlarged-photo with the dimensions of the original photo to check which has a constant ratio.
Step 2:
The original photo was a 4-inch by 5-inch photo.
Option 1 is 7-inch by 9-inch, so the ratios are
The ratios are different so this cannot be the enlarged photo's dimensions.
Option 2 is 8-inch by 10-inch, so the ratios are
The ratios are the same so this can be the enlarged photo's dimensions.
Option 3 is 12-inch by 16-inch, so the ratios are
The ratios are different so this cannot be the enlarged photo's dimensions.
So the enlarged-photo with dimensions of 8-inch by 10-inch should be picked.
Answer:
Yes, it would be unusual.
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.
If or
, the outcome X is considered unusual.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
Would it be unusual for this sample mean to be less than 19 days?
We have to find Z when X = 19. So
By the Central Limit Theorem
, so yes, the sample mean being less than 19 days would be considered an unusual outcome.