Answer:
Step-by-step explanation:
We want to describe the solution set on the number line as an inequality.
We have open circles at both ends.
This means the inequalities are not the ones containing equal sign.
The number line started from -3 and ended at 13 non inclusive.
This means the solution set for the inequality are all real numbers greater than -3 but less than 13.
We write this as:
Answer:
0.71% probability that the daily average amount of radiation received by a rover will exceed 102
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 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 problem, we have that:
What is the probability that the daily average amount of radiation received by a rover will exceed 102?
This is 1 subtracted by the pvalue of Z when X = 102. So
By the Central Limit Theorem
has a pvalue of 0.9929
1 - 0.9929 = 0.0071
0.71% probability that the daily average amount of radiation received by a rover will exceed 102
