The normal temperature range for Yuma, AZ on January 11 is at least 48 degrees but no higher than 64 degrees Fahrenheit. Which i
1 answer:
Answer: Our required interval for temperature is
Step-by-step explanation:
Since we have given that
The normal temperature range for Yuma, on Janurary is atleast = 48 degrees
and the highest temperature on that day is no higher than 64 degrees.
Let the temperature in Yuma be 'x'.
So, we know that for atleast means it can 48 degrees or more, and no higher than means it should be equa to or less than 64 degrees.
Mathematically, it is expressed as
Hence, our required interval for temperature is
You might be interested in
Answer:
0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.
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 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.
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
Proportion of 0.6
This means that
Sample of 46
This means that
Mean and standard deviation:
Probability of obtaining a sample proportion less than 0.5.
p-value of Z when X = 0.5. So
By the Central Limit Theorem
has a p-value of 0.0838
0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.