Question

Suppose we have a binomial experiment in which success is defined to be a particular quality...

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

(a)

  • Suppose n = 45 and
  • p = 0.38.

(For each answer, enter a number. Use 2 decimal places.)
n·p =
n·q =

Can we approximate by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, _____ be approximated by a normal random variable because _____ _____.

first blank

Yes No    

second blank

can cannot    

third blank

n·q exceeds n·p does not exceed     n·p and n·q do not exceed n·p exceeds both n·p and n·q exceed n·q does not exceed

fourth blank (Enter an exact number.)


What are the values of μ and σ? (For each answer, enter a number. Use 3 decimal places.)
μ = mu sub p hat =

σ = sigma sub p hat =

(b)

Suppose

  • n = 25 and
  • p = 0.15.

Can we safely approximate by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, _____ be approximated by a normal random variable because _____ _____.

first blank

Yes No    

second blank

can cannot    

third blank

n·q exceeds n·p does not exceed     n·p and n·q do not exceed n·p exceeds both n·p and n·q exceed n·q does not exceed

fourth blank (Enter an exact number.)

(c)

Suppose

  • n = 52 and
  • p = 0.29.

(For each answer, enter a number. Use 2 decimal places.)
n·p =
n·q =

Can we approximate by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, _____ be approximated by a normal random variable because _____ _____.

first blank

Yes No    

second blank

can cannot    

third blank

n·q exceeds n·p does not exceed     n·p and n·q do not exceed n·p exceeds both n·p and n·q exceed n·q does not exceed

fourth blank (Enter an exact number.)


What are the values of μ and σ? (For each answer, enter a number. Use 3 decimal places.)
μ = mu sub p hat =

σ = sigma sub p hat =

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