probability of normal distribution and binomial distribution

3. A production line manufactures 1000 ohms resistors that must satisfy a 10% tolerance.

a. If a resistance is adequately described by a Gaussian random variable for which mean = 1000; and standard deviation = 40;, what fraction of the resistance expected to be rejected?

b. If a machine is not properly adjusted, the product resistances changes, the case where mean= 1050; (5% shift). What fraction is now rejected?

4. At a certain military installation six similar radars are placed in operation. It is known that radar's probability of failing to operate before 500 hours of "on" time have accumulated is 0.06. What are the probabilities that, before 500 hours have elapsed, (a) all will operate, (b) all will fail, and (c) only one will fail?

It seems the equations could be displayed. Please see the attached file.
Answer to 3: Since the resistance follows the normal function, the probability function is

To calculate the rejection rate of 10% from the mean, we could calculate the acceptation rate first, i.e. the rate the ...

Solution Summary

The solution is comprised of detailed explanations of calculation of probabilities under nomral distribution and binomial distribution.

Find the indicated probabilities.
a. P (z > -0.89)
b. P (0.45 < z < 2.15)
Write the binomialprobability as a normalprobability using the continuity correction.
BinomialProbabilityNormalProbability
c. P ( x ≤ 56) P ( x < ? )
d. P ( x = 69 ) P ( ? < x < ?

h-p is said to be the leading seller of pc's in the U.S WITH 27% share of the pc market. if a researcher selects 130 recent pc purchases, use the normal approximation to the binomial to find the probability that more than 39 bought a h-p computer

Answer the following:
(A) Find the binomialprobability P(x = 6), where n = 15 and p = 0.60.
(B) Set up, without solving, the binomialprobability P(x is at most 6) using probability notation.
(C) How would you find the normal approximation to the binomialprobability P(x = 6) in part A? Please show how you would calculate

Consider a binomialdistribution with 15 identical trials, and a probability of success of 0.5.
Find the probability that x = 2 using the binomial tables.
Use the normal approximation to find the probability that x = 2

Nathan wants to approximate a binomialprobability by normal curve areas. The number of trials is 50 and the probability of success for each trial is 0.95.
Can Nathan use the normal curve area to approximate a binomialprobability?

Nathan wants to approximate a binomialprobability by normal curve areas. The number of trials is 50 and the probability of success for each trial is 0.95
Can Nathan use the normal curve area to approximate a binomialprobability?

If np ≥ 5 and nq ≥ 5 estimate P (fewer than 2) with n= 13 and p= 0.4 by using the normaldistribution as an approximation to the binomialdistribution if np < 5 or nq <5 then state that the normal approximation is not suitable.
Select the correct choice below and if necessary fill in the answer box to complete our choic

Consider a binomialdistribution with 15 identical trials, and a probability of success of 0.5
i. Find the probability that x = 2 using the binomial tables
ii. Use the normal approximation to find the probability that x = 2. Show all work

It is estimated that the probability that the general population will live past their 85th birthday is 5.4%. Use the standard normaldistribution to approximate this Binomial problem and answer the following questions.
Out of a sample of 600, what is the probability that fewer than 30 will live beyond their 85th birthday?

Assume a binomialprobabilitydistribution has µ=0.60 and n= 200
a. What is the mean and standard deviation?
b. Is this a situation in which binomial probabilities can be approximated by the normalprobabilitydistribution? Explain
c. What is the probability of 100 to 110 successes?
d. What is the probability of 130 or