Spin the spinner 90 times to simulate the 90-day weather forecast. Which type of weather has the lowest observed frequency?
2 answers:
Complete Question:
The weather forecast for next season calls for a 10% chance of wind, a 20% chance of rain, a 30% chance of clouds, and a 40% chance of sunshine. If there are 90 days in the season,spin the spinner 90 times to simulate the 90-day weather forecast. Which type of weather has the lowest observed frequency?
Answer:
Wind Weather
Step-by-step explanation
From the question above
The sample space(which means the total number of events that we are considering ) = 90 times of spinning which represents the 90 days weather forecast
The chance of wind weather occurring is 10% and its observed frequency of occurrence within the 90 days is = = 9 days
The chance of rain weather occurring is 20% and its observed frequency of occurrence within the 90 days is = = 18 days
The chance of cloud weather occurring is 30% and its observed frequency of occurrence within the 90 days is = = 27 days
The chance of sunshine weather occurring is 40% and its observed frequency of occurrence within the 90 days is = = 36 days
We see from the above calculation that the weather with the lowest observed frequency is Wind weather
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Let X be the length of rulers. X follows Normal distribution with mean μ and standard deviation σ = 0.02. A sample of size n=4 is drawn from population and sample mean m=1000. We have to find 90% confidence interval for population mean μ.
Here population standard deviation is given to us so we will use z confidence interval for mean. It is given as
(Sample mean - Margin of error , Sample mean + Margin of error)
Where margin of error for z confidence interval is
ME = σ
Where σ = population standard deviation = 0.02
n= sample size =4
= Critical z score value for given confidence level
We have to find here 90% confidence interval so confidence level c= 0.9
α = 1 -c =1-0.9 = 0.1
=
=
Here we have to find z score value such that area below it is -z is 0.05 and above z is 0.05
Using excel function to find z score value
=NORM.S.INV(0.05) = -1.645
For calculating confidence interval we consider positive z score value which is 1.645
So the margin of error is
ME =
ME = 0.01645
90% confidence interval for mean is
(Sample mean - ME, Sample mean+ME)
1000- 0.01645, 1000+0.01645
(1000.01645, 999.9836)
Rounding interval upto 3 decimal places
(1000.016, 999.984)
90% confidence interval for population mean is (1000.016, 999.984)