Question 1

When approximating $B(40,0.45)$ by $N(\mu, \sigma^2 )$, what is the value of $\mu$?

Accepted Answer

18

Question 2

When approximating $B(40,0.45)$ by $N(\mu, \sigma^2 )$, what is the value of $\sigma^2$ in decimal form?

Accepted Answer

9.9

Question 3

Which of the following is a condition under which the binomial distribution can be approximated by the normal distribution?

Accepted Answer

Large $n$

Answer

Large $p$

Answer

Small $p$

Answer

Small $n$

Question 4

Which of the following is a condition under which the binomial distribution can be approximated by the normal distribution?

Accepted Answer

$p \approx 0.5$

Answer

$p \approx 0$

Answer

$p \approx 1$

Question 5

$Y$ is a normal approximation to the binomial distribution $X$. What is the value of $a$ in the following? $P(X>5) \approx P(Y>a)$

Accepted Answer

5.5

Question 6

$Y$ is a normal approximation to the binomial distribution $X$. What is the value of $a$ in the following? $P(X<10) \approx P(Y<a)$

Accepted Answer

9.5

Question 7

$Y$ is a normal approximation to the binomial distribution $X$. What is the value of $a$ in the following? $P(X \leq 17) \approx P(Y<a)$

Accepted Answer

17.5

Question 8

$Y$ is a normal approximation to the binomial distribution $X$. What is the value of $a$ in the following? $P(X \geq 23) \approx P(Y>a)$

Accepted Answer

22.5

Question 9

$X \sim B(50, 0.6)$. Use the normal distribution to calculate an approximation for $P(X>34)$. Give your answer correct to 4 decimal places.

Accepted Answer

0.0970

Question 10

$X \sim B(105, 0.55)$. Use the normal distribution to calculate an approximation for $P(X<52)$. Give your answer correct to 4 decimal places.

Accepted Answer

0.1101

Question 11

$X \sim B(240, 0.4)$. Use the normal distribution to calculate an approximation for $P(X \leq 99)$. Give your answer correct to 4 decimal places.

Accepted Answer

0.6777

Question 12

$X \sim B(500, 0.36)$. Use the normal distribution to calculate an approximation for $P(X \geq 187)$. Give your answer correct to 4 decimal places.

Accepted Answer

0.2724

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