A TV executive is interested in the popularity of a particular cable TV show. She has been told that a whopping 68% of American
1 answer:
Answer:
0.0989 = 9.89% probability that all 6 of the households in her city being monitored by the TV industry would tune in to the new show
Step-by-step explanation:
For each household, there are only two possible outcomes. Either they will tune in to the show, or they wont. The probability of a household being tuned in to the show is independent of any other household. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
She has been told that a whopping 68% of American households would be interested in tuning in to a new network version of the show.
This means that
If this is correct, what is the probability that all 6 of the households in her city being monitored by the TV industry would tune in to the new show
All 6 is when
. So
0.0989 = 9.89% probability that all 6 of the households in her city being monitored by the TV industry would tune in to the new show
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Answer:
3
Step-by-step explanation:
The measure of the slope is at x = a
Differentiate using the power rule
(a
) = na
Given
y = x³ - 1, then
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The slope at (1, 0) is
= 3(1)² = 3
Answer:
a) 51.60% probability that in a given year there will be less than 21 earthquakes.
b) 49.35% probability that in a given year there will be between 18 and 23 earthquakes.
Step-by-step explanation:
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.
In this problem, we have that:
a) Find the probability that in a given year there will be less than 21 earthquakes.
This is the pvalue of Z when X = 21. So
has a pvalue of 0.5160.
So there is a 51.60% probability that in a given year there will be less than 21 earthquakes.
b) Find the probability that in a given year there will be between 18 and 23 earthquakes.
This is the pvalue of Z when X = 23 subtracted by the pvalue of Z when X = 18. So:
X = 23
has a pvalue of 0.7611
X = 18
has a pvalue of 0.2676
So there is a 0.7611 - 0.2676 = 0.4935 = 49.35% probability that in a given year there will be between 18 and 23 earthquakes.