Respuesta :
X ~ Bin ( n , p)
The probability that a random sample of 60 households will have exactly 20 households with 3 or more vehicles is 0.90931
What is mean and standard deviation?
- Continuous data, not categorical data, are summarised using the standard deviation in conjunction with the mean.
- Additionally, the standard deviation, like the mean, is typically only acceptable when the continuous data does not have outliers or is not highly skewed.
- A common way to assess variability in statistics is the standard deviation (SD). It displays the degree of variance from the average (mean). When the SD is low, the data tend to be close to the mean, while when it is high, the data are dispersed over a wide range of values.
Using Normal Approximation to Binomial
Mean = n * P = ( 60 * 0.3 ) = 18
Variance = n * P * Q = ( 60 * 0.3 * 0.7 ) = 12.6
Standard deviation = √(variance) = √(12.6) = 3.5496
P ( X = 20 )
Using continuity correction
P( n - 0.5 < X < n + 0.5 )
= P ( 20 - 0.5 < X < 20 + 0.5 )
= P ( 19.5 < X < 20.5 )
Using EXCEL,
P ( 19.5 < X < 20.5 )
= P(X < 20.5) - P(X < 19.5)
= BINOM.DIST ( 20.5 , 60 , 0.30, TRUE) - BINOM.DIST ( 19.5 , 60 , 0.30, TRUE)
= 0.7622 - 0.66916
= 0.0931
Hence, the probability that a random sample of 60 households will have exactly 20 households with 3 or more vehicles is 0.90931
To know more about mean check the below link:
https://brainly.com/question/1136789
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