Question

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

(a)

• Suppose n = 33 and
• p = 0.37.

(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

a. n·p and n·q do not exceed

b. n·p does not exceed    

c. n·q does not exceedboth

d. n·p and n·q exceed

e. n·q exceeds

f. n·p exceeds

fourth blank (Enter an exact number.)


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

σ_p̂ = sigma sub p hat =

(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

a. n·p and n·q do not exceed

b. n·p does not exceed     

c. n·q does not exceedboth

d. n·p and n·q exceed

e. n·q exceeds

f. n·p exceeds

fourth blank (Enter an exact number.)

2. Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dl. Recently, the patient's total calcium tests gave the following readings (in mg/dl). Assume that the population of x values has an approximately normal distribution.

10.1

9.0

10.5

8.9

9.4

9.8

10.0

9.9

11.2

12.1

(a)

Use a calculator with mean and sample standard deviation keys to find the sample mean reading  and the sample standard deviation s. (in mg/dl; round your answers to two decimal places.)
=  mg/dl
s =  mg/dl

(b)

Find a 99.9% confidence interval for the population mean of total calcium in this patient's blood. (in mg/dl; round your answer to two decimal places.)
lower limit          mg/dl
upper limit          mg/dl

(c)

Based on your results in part (b), do you think this patient still has a calcium deficiency? Explain.

Yes. This confidence interval suggests that the patient may still have a calcium deficiency.Yes. This confidence interval suggests that the patient no longer has a calcium deficiency.     No. This confidence interval suggests that the patient may still have a calcium deficiency.No. This confidence interval suggests that the patient no longer has a calcium deficiency.

(c)

Suppose

• n = 45 and
• p = 0.18.

(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

a. n·p and n·q do not exceed

b. n·p does not exceed     

c. n·q does not exceedboth

d. n·p and n·q exceed

e. n·q exceeds

f. n·p exceeds

fourth blank (Enter an exact number.)
_______

Answer 1

, be approximated by a normal random variable because

, be approximated by a normal random variable because

, be approximated by a normal random variable because

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