Standard Deviation Word Problems

**Page 1**

1.

Find the probability that a student can guess 60% or less of the answers correctly in a 40 question true false examination.

a. | 92.27% | ||

b. | 13.41% | ||

c. | 36.59% | ||

d. | 86.59% |

For a random variable

Since both the conditions are satisfied, the random variable

Mean μ

Standard deviation σ

Continuity correction =

To convert the

P(

The probability that a student can guess 60% or more of the answers correctly in a 40 question true false examination is 92.27%.

Correct answer : (1)

2.

It has been found that 6% of the tools produced by a certain machine are defective. What is the probability that in a shipment of 500 such tools 6% or more will prove defective?

a. | 6% | ||

b. | 53.98% | ||

c. | 3.98% | ||

d. | 0.54% |

For a random variable

Since both the conditions are satisfied, the random variable

Mean μ

Standard deviation σ

Continuity correction =

To convert the

P(

The probability that in a shipment of 500 such tools 6% or more will prove defective is 53.98%.

Correct answer : (2)

3.

It has been found that 6% of the tools produced by a certain machine are defective. What is the probability that in a shipment of 500 such tools 4% or less will prove defective?

a. | 97.13% | ||

b. | 0.97% | ||

c. | 2.87% | ||

d. | 47.13% |

For a random variable

Since both the conditions are satisfied, the random variable

Mean μ

Standard deviation σ

Continuity correction =

To convert the

P(

The probability that in a shipment of 500 such tools 4% or less will prove defective is 2.87%.

Correct answer : (3)

4.

The election results showed that a certain candidate received 44% of the votes. Determine the probability that a poll of 500 people selected at random from the voting population would have shown a majority of votes in favor of the candidate.

a. | 49.71% | ||

b. | 0.29% | ||

c. | 0.0029% | ||

d. | 99.71% |

For a random variable

Since both the conditions are satisfied, the random variable

Mean μ

Standard deviation σ

Continuity correction =

To get a majority, the candidate should get more than 50% of the votes. That is

To convert the

P(

The probability that the voting population would have shown a majority of votes in favor of the candidate is 0.0029 or 0.29%.

Correct answer : (2)

5.

Find the probability that of the next 300 children born, 60% or greater will be boys. Assume equal probabilities for the births of boys and girls.

a. | 50.04% | ||

b. | 99.96% | ||

c. | 49.96% | ||

d. | 0.04% |

[Equal probabilities for the births of boys and girls.]

For a random variable

Since both the conditions are satisfied, the random variable

Mean μ

Standard deviation σ

Continuity correction =

To convert the

P(

The probability that of the next 300 children born, 60% or greater will be boys is 0.04%.

Correct answer : (4)

6.

The probability that a student has access to Internet from his/her home is 40%. If a random sample of 100 students is selected, then find the probability that between 50% and 60% of the students have access to Internet from their home.

a. | 2.61% | ||

b. | 0.026% | ||

c. | 97.39% | ||

d. | 26.1% |

For a random variable

Since both the conditions are satisfied, the random variable

Mean μ

Standard deviation σ

Continuity correction =

We subtract 0.005 from the left

P(0.5 ≤

The probability that between 50% and 60% of the students have access to Internet from their home is 2.61%.

Correct answer : (1)

7.

Find the probability that of the next 100 children born, 40% or less will be boys. Assume equal probabilities for the births of boys and girls.

a. | 1.78% | ||

b. | 98.22% | ||

c. | 2.87% | ||

d. | 97.13% |

[Equal probabilities for the births of boys and girls.]

For a random variable

Since both the conditions are satisfied, the random variable

Mean μ

Standard deviation σ

Continuity correction =

To convert the

P(

The probability that of the next 100 children born, 40% or less will be boys is 2.87%.

Correct answer : (3)

8.

Find the probability that of the next 200 children born, between 45% and 60% will be girls. Assume equal probabilities for the births of boys and girls.

a. | 43.31% | ||

b. | 49.82% | ||

c. | 6.51% | ||

d. | 93.13% |

[Equal probabilities for the births of boys and girls.]

For a random variable

Since both the conditions are satisfied, the random variable

Mean μ

Standard deviation σ

Continuity correction =

We subtract 0.0025 from the left

P(0.45 ≤

The probability that of the next 200 children born, between 45% and 60% will be girls is 93.13%.

Correct answer : (4)

9.

If $p$ = 0.50 and $n$ = 100, what is the value of μ_{$\stackrel{\u02c6}{p}$}, σ _{$\stackrel{\u02c6}{p}$}?

a. | 50.0, 5.0 | ||

b. | 0.50, 0.05 | ||

c. | 0.50, 5.0 | ||

d. | 0.50, 0.50 |

For a random variable

Since both the conditions are satisfied, the random variable

Mean μ

Standard deviation σ

So, the mean and standard deviation are 0.50, 0.05 respectively.

Correct answer : (2)

10.

Suppose $n$ = 50 and $p$ = 0.35. Can we safely approximate $\stackrel{\u02c6}{p}$ by a normal distribution? What is the value of the continuity correction?

a. | Yes, 0.01 | ||

b. | Yes, 25 | ||

c. | Yes, 0.07 | ||

d. | No, 0.01 |

For a random variable

Since both the conditions are satisfied, the random variable

Continuity correction =

So, the continuity correction is 0.01.

Correct answer : (1)