Sorry but where is the question
To find probability you have to add the samples that are included. In this situation, you add 240+210. Then you get 450. Then you divide heads by 450 to get the probability.
The probability is 240/450, which is 53%
In fractions it is 53 1/3.
You could use 4(division) sign 25 + 3 (division sign) 15 * 10, ok?
Answer: a) α = 0.7927, b) at u=14.8, β = 0.99767, at u = 14.9, β= 0.2073
Step-by-step explanation: a) from the question, u= population mean = 15 and x= sample mean = 14.9
σ = population standard deviation = 0.5, n = sample size = 50.
We get the probability of committing a type 1 error by using the z score.
Z = x - u/(σ/√n)
Z = 14.9 - 15/(0.5/√50)
Z = - 0.1/0.0707
Z = - 1.41.
By checking the the probabilistic value attached to this z score using a standard normal distribution table whose area is to the left of the distribution, we have that
P(z=-1.41) = 0.7927.
Hence the probability of committing a type 1 error is 0.7927
b)
at x = 14.8 ( I let ua=x=14.8)
Z = x - u/(σ/√n)
Z = 14.8 - 15/(0.5/√50)
Z = - 0.2/ 0.0707
Z = - 2.83
Using the standard normal distribution table, we have that
P(z=-2.38) = 0.00233.
But α + β = 1
Where α= probability of committing a type 1 error
β = probability of committing a type 2 error.
β = 1 - α
β = 1 - 0.00233
β = 0.99767
At x = 14.9
Z = x - u/(σ/√n)
Z = 14.9 - 15/(0.5/√50)
Z = - 0.1/0.0707
Z = - 1.41.
P(z=-1.41) = 0.7927.
α = 0.7927.
But α + β = 1
β = 1 - 0.7927
β = 0.2073
1/52 because there is only one 7 of hearts in the 52 cards.
