Question

Use the Normal Approximation to the Binomial Distribution to compute the probability of passing a true/false test of 40 questions if the minimum passing grade is 60% and all responses are random guesses.

Answer #1

Answer)

N = 40

P = 0.5 (as there are two options and only one among those 2, will be correct so probability of getting a correct response is 1/2 = 0.5)

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 20

N*(1-p) = 20

Both the conditions are met so we can use standard normal z table to estimate the probability

z= (oberved p - claimed p)/standard error

Standard error = √{claimed p*(1-claimed p)/√n

Observed P = 0.6 (60%)

Claimed P = 0.5

N = 40

After substitution

Z = 1.26

From z table, P(z>1.26) = 0.1038

Use normal approximation (without continuity correction) to
estimate the probability of passing a true/false test of 30
questions if the minimum passing grade is 60% and all responses are
random guesses.

Use normal approximation (without continuity correction) to
estimate the probability of passing a true/false test of 20
questions if the minimum passing grade is 60% and all responses are
random guesses.

Use normal approximation to estimate the probability of passing a
true/false test of 30 questions if the minimum passing grade is 90%
and all responses are random guesses.

Normal Approximation to Binomial
Assume n = 100, p = 0.4.
Use the Binomial Probability function to compute the P(X =
40)
Use the Normal Probability distribution to approximate the P(X
= 40)
Are the answers the same? If not, why?

Statistics
True/False For a binomial probability experiment, with n = 60
and p =.2, it is appropriate to use the normal approximation to the
binomial distribution without continuity correction.

True or False?
19. In a binomial distribution the random variable X is
discrete.
20. The standard deviation and mean are the same for the
standard normal distribution.
21. In a statistical study, the random variable X = 1, if the
house is colonial and X = 0 if the house is not colonial, then it
can be stated that the random variable is continuous. 22. For a
continuous distribution, P(X ≤ 10) is the same as P(X<10).
23. For...

1. Normal Approximation to Binomial Assume
n = 10, p = 0.1.
a. Use the Binomial Probability function to compute the P(X =
2)
b. Use the Normal Probability distribution to approximate the
P(X = 2)
c. Are the answers the same? If not, why?

A pair of dice is rolled 240 times. Use the normal approximation
to binomial distribution the probability that a total of 7
occurs
(a) at least 35 times?
(b) between 36 and 44 times inclusive?
(c) exactly 40 times?

A binomial distribution has p? = 0.26 and n? = 76. Use the
normal approximation to the binomial distribution to answer parts
?(a) through ?(d) below.
?a) What are the mean and standard deviation for this?
distribution?
?b) What is the probability of exactly 15 ?successes?
?c) What is the probability of 14 to 23 ?successes?
?d) What is the probability of 11 to 18 ?successes

A die is tossed 120 times. Use the normal curve approximation to
the binomial distribution to find the probability of getting the
following result. More than 18 5 's

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