Advertisements
Advertisements
प्रश्न
X is normally distributed with mean 12 and SD 4. Find P(X ≤ 20) and P(0 ≤ X ≤ 12)
Advertisements
उत्तर
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
संबंधित प्रश्न
Derive the mean and variance of binomial distribution
If 5% of the items produced turn out to be defective, then find out the probability that out of 20 items selected at random there are find the mean and variance
In a particular university 40% of the students are having newspaper reading habit. Nine university students are selected to find their views on reading habit. Find the probability that none of those selected have newspaper reading habit
An experiment succeeds twice as often as it fails, what is the probability that in next five trials there will be at least three successes
In a photographic process, the developing time of prints may be looked upon as a random variable having the normal distribution with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability that it will take less than 16.35 seconds to develop prints
Choose the correct alternative:
Which of the following statements is/are true regarding the normal distribution curve?
Choose the correct alternative:
The weights of newborn human babies are normally distributed with a mean of 3.2 kg and a standard deviation of 1.1 kg. What is the probability that a randomly selected newborn baby weight less than 2.0 kg?
A manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected because they are either oversize or undersize. What is the probability that a batch of 10 pistons will contain at least 2 rejects?
If electricity power failures occur according to a Poisson distribution with an average of 3 failures every twenty weeks, calculate the probability that there will not be more than one failure during a particular week
Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Raghul wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Raghul takes the test and scores 585. Will he be admitted to this university?
