In: Statistics and Probability
Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.
(a) Suppose n = 43 and p = 0.36.
(For each answer, enter a number. Use 2 decimal places.)
n·p =
n·q =
Can we approximate p̂ by a normal distribution? Why? (Fill
in the blank. There are four answer blanks. A blank is represented
by _____.)
_____, p̂ _____ be approximated by a normal random
variable because _____ _____.
first blank
Yes or No
second blank
can or cannot
third blank
n·p exceeds
n·p and n·q do not exceed
n·q exceeds
n·p does not exceed
n·q does not exceed
both n·p and n·q exceed
fourth blank (Enter an exact number.)
__________
What are the values of μp̂ and
σp̂? (For each answer, enter a number.
Use 3 decimal places.)
μp̂ =
σp̂ =
(b) Suppose n = 25 and p = 0.15.
Can we safely approximate p̂ by a normal distribution?
Why or why not? (Fill in the blank. There are four answer blanks. A
blank is represented by _____.)
_____, p̂ _____ be approximated by a normal random
variable because _____ _____.
first blank
Yes or No
second blank
can or cannot
third blank
n·p exceeds
n·p and n·q do not exceed
n·q exceeds
n·p does not exceed
n·q does not exceed
both n·p and n·q exceed
fourth blank (Enter an exact number.)
_____
(c) Suppose n = 56 and p = 0.19.
(For each answer, enter a number. Use 2 decimal places.)
n·p =
n·q =
Can we approximate p̂ by a normal distribution? Why? (Fill
in the blank. There are four answer blanks. A blank is represented
by _____.)
_____, p̂ _____ be approximated by a normal random
variable because _____ _____.
first blank
Yes or No
second blank
can or cannot
third blank
n·p exceeds
n·p and n·q do not exceed
n·q exceeds
n·p does not exceed
n·q does not exceed
both n·p and n·q exceed
fourth blank (Enter an exact number.)
_____
What are the values of μp̂ and
σp̂? (For each answer, enter a number.
Use 3 decimal places.)
μp̂ =
σp̂ =
, be approximated by a normal random variable because
, be approximated by a normal random variable because
, be approximated by a normal random variable because