Advertisements
Advertisements
Question
X is normally distributed with mean 12 and SD 4. Find P(X ≤ 20) and P(0 ≤ X ≤ 12)
Advertisements
Solution
X is normally distribution with mean 12 and SD 4
∴ µ = 12 and σ = 4
Standard normal variable
z = `(x - mu)/sigma`
= `(x - 12)/4`
P(X ≤ 20)
When x = 20
z = `(20 - 12)/4 = 8/4` = 2
v(x ≤ 20) = `8/4` = 2
P(x ≤ 20) = P(z ≤ 2)
= 0.5 + p(0 < z < 2)
= 0.5 + 0.4772
= 0.9772
P(0 ≤ X ≤ 12)
When x = 0
z = `(0 - 12)/4 = (-12)/4 = - 3`
When x = 12
z = `(12 - 12)/4 = 0/4` = 0
P(0 ≤ x ≤ 12) = P(-3 ≤ z ≤ 0)
= P(0 ≤ z ≤ 3)
= 0.4987
APPEARS IN
RELATED QUESTIONS
Among 28 professors of a certain department, 18 drive foreign cars and 10 drive local made cars. If 5 of these professors are selected at random, what is the probability that atleast 3 of them drive foreign cars?
Write the conditions for which the poisson distribution is a limiting case of binomial distribution
Derive the mean and variance of poisson distribution
The average number of phone calls per minute into the switchboard of a company between 10.00 am and 2.30 pm is 2.5. Find the probability that during one particular minute there will be atleast 5 calls
If the heights of 500 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches, how many students have height less than or equal to 64 inches
Choose the correct alternative:
If Z is a standard normal variate, the proportion of items lying between Z = – 0.5 and Z = – 3.0 is
Choose the correct alternative:
In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is
Choose the correct alternative:
In a binomial distribution, the probability of success is twice as that of failure. Then out of 4 trials, the probability of no success is
Vehicles pass through a junction on a busy road at an average rate of 300 per hour. Find the probability that none passes in a given minute
Vehicles pass through a junction on a busy road at an average rate of 300 per hour. What is the expected number passing in two minutes?
