Tamara is planting bushes around her house. So far today she has planted 5 bushes and she wants to plant at least 12 bushes toda
1 answer:
Answer:
Step-by-step explanation:
Given:
Number of bushes planted = 5
Minimum number of bushes to be planted = 12
Let the number of bushes planted after planting 5 bushes be .
Since, Tamara has already planted 5 bushes, total number of bushes planted is given as:
Now, as per question, total number of bushes should be 12 or greater than 12.
Therefore, .
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Answer:
96.42% probability that the number of tails is between 40 and 60.
Step-by-step explanation:
I am going to use the binomial approximation to the normal to solve this question.
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:
100 tosses, so
Two outcomes, both equally as likely. So
So
Estimate the approximate probability that the number of tails is between 40 and 60.
Using continuity correction.
This is the pvalue of Z when X = 60.5 subtracted by the pvalue of Z when X = 39.5. So
X = 60.5
has a pvalue of 0.9821
X = 39.5
has a pvalue of 0.0179
0.9821 - 0.0179 = 0.9642
96.42% probability that the number of tails is between 40 and 60.