Which of the following data sets has a range of 40?
2 answers:
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Answer: 0.0170
Step-by-step explanation:
Given : The mean amount purchased by a typical customer at Churchill’s Grocery Store is $23.50, with a standard deviation of $5.00.
i.e.
We assume the distribution of amounts purchased follows the normal distribution.
Sample size : n=50
Let be the sample mean.
Formula :
Then, the probability that the sample mean is at least $25.00 will be :-
Hence, the likelihood the sample mean is at least $25.00= 0.0170
Answer:
5.05% probability that no more than 34% had received such an email.
Step-by-step explanation:
We use the binomial approximation to the normal to solve this problem.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be 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.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
In a random sample of 700 adults, what is the probability that no more than 34% had received such an email?
34% is 0.34*700 = 238
So this probability is the pvalue of Z when X = 238.
has a pvalue of 0.0505
5.05% probability that no more than 34% had received such an email.