Lesson 6.4 Checkpoint

The makers of Skittles claim that 20% of Skittles candies are orange. You select a random sample of 20 Skittles from a large bag. Let p̂ = the proportion of orange Skittles in the sample. Calculate the mean of the sampling distribution of p̂.

(LT 6.4.1 #1)

• μ_p̂ = 0.20

• μ_p̂ = 20

• μ_p̂ = 4

• μ_p̂ = 0.05

The makers of Skittles claim that 20% of Skittles candies are orange. You select a random sample of 20 Skittles from a large bag. Let p̂ = the proportion of orange Skittles in the sample. Calculate the standard deviation of the sampling distribution of p̂.

(LT 6.4.1 #2)

• σ_p̂ = 8.9

• σ_p̂ = 0.089

• σ_p̂ = 0.20

• σ_p̂ = 1.789

The makers of Skittles claim that 20% of Skittles candies are orange. You select a random sample of 20 Skittles from a large bag. Let p̂ = the proportion of orange Skittles in the sample. Interpret the standard deviation of the sampling distribution of p̂, σ_p̂ = 0.089.

(LT 6.4.1 #3)

• In SRSs of size n = 20, the sample proportion of orange Skittles will typically vary by about 0.089 from the true proportion of p = 0.20.

• In SRSs of size n = 20, the sample proportion of orange Skittles will typically vary by about 0.20 from the true proportion of p = 0.089.

• In SRSs of size n = 0.20, the sample proportion of orange Skittles will typically vary by about 0.089 from the true proportion of p = 20.

• In SRSs of size n = 20, the sample proportion of orange Skittles will typically vary by about 0.089 from the true proportion of p = 20.

The Transportation Security Administration is responsible for airport safety. On some flights, TSA officers randomly select passengers for an extra security check before boarding. One such flight had 120 passengers - 16 in first class and 104 in coach class. TSA officers selected as SRS of 10 passengers for screening. Would it be appropriate to use a normal distribution to model the sampling distribution of p̂ = the proportion of first-class passengers in the sample? Justify your answer

(LT 6.4.2 #1)

• Yes, because np = 10(0.13) = 1.33 ≥ 10 and n(1-p) = 10(0.87) = 87 ≥ 10, the sampling distribution of p̂ is approximately normal.

• Yes, because np = 10(0.13) = 1.33 < 10 and n(1-p) = 10(0.87) = 87 ≥ 10, the sampling distribution of p̂ is approximately normal.

• No, because np = 10(0.13) = 1.33 ≥ 10 and n(1-p) = 10(0.87) = 87 ≥ 10, the sampling distribution of p̂ is not approximately normal.

• No, because np = 10(0.13) = 1.33 < 10 and n(1-p) = 10(0.87) = 87 ≥ 10, the sampling distribution of p̂ is not approximately normal.

In the game of Scrabble, each player begins by drawing 7 tiles from a bag containing 100 tiles. There are 42 vowels, 56 consonants, and 2 blank tiles in the bag. Cait chooses an SRS of 7 tiles. Would it be appropriate to use a normal distribution to model the sampling distribution of p̂ = the proportion of vowels in her sample? Justify your answer

(LT 6.4.2 #2)

• Yes, because np = 7(0.42) = 2.94 ≥ 10 and n(1-p) = 7(0.58) = 4.06 ≥ 10, the sampling distribution of p̂ is approximately normal.

• Yes, because np = 7(0.42) = 2.94 < 10 and n(1-p) = 7(0.58) = 4.06 ≥ 10, the sampling distribution of p̂ is approximately normal.

• No, because np = 7(0.42) = 2.94 ≥ 10 and n(1-p) = 7(0.58) = 4.06 ≥ 10, the sampling distribution of p̂ is not approximately normal.

• No, because np = 7(0.42) = 2.94 < 10 and n(1-p) = 7(0.58) = 4.06 < 10, the sampling distribution of p̂ is not approximately normal.

A large mail-order company advertises that it ships 90% of its orders within 3 working day. You select as SRS of 100 of the orders received in the past week for an audit. Let p̂ = the proportion of orders in the last week that were shipped within 3 working days. Would it be appropriate to use a normal distribution to model the sampling distribution of p̂ = the proportion of orders in the last week that were shipped within 3 working days? Justify your answer

(LT 6.4.2 #3)

• Yes, because np = 100(0.90) = 90 ≥ 10 and n(1-p) = 100(0.10) = 10 ≥ 10, the sampling distribution of p̂ is approximately normal.

• Yes, because np = 100(0.90) = 90< 10 and n(1-p) = 100(0.10) = 10 ≥ 10, the sampling distribution of p̂ is approximately normal.

• No, because np =100(0.90) = 90 ≥ 10 and n(1-p) = 100(0.10) = 10 ≥ 10, the sampling distribution of p̂ is not approximately normal.

• No, because np = 100(0.90) = 90 < 10 and n(1-p) = 100(0.10) = 10 < 10, the sampling distribution of p̂ is not approximately normal.

According to a recent U.S. Bureau of Labor Statistics report, the proportion of married couples with children in which both parents work outside of the home is 59%. You select an SRS of 50 married couples with children and let p̂ = the sample proportion of couples in which both parents work outside of the home. Would it be appropriate to use a normal distribution to model the sampling distribution of p̂ = the sample proportion of couples in which both parents work outside of the homes? Justify your answer

(LT 6.4.2 #4)

• Yes, because np = 50(0.59) = 29.5 ≥ 10 and n(1-p) = 50(0.41) = 20.5 ≥ 10, the sampling distribution of p̂ is approximately normal.

• Yes, because np = 50(0.59) = 29.5 < 10 and n(1-p) = 50(0.41) = 20.5 ≥ 10, the sampling distribution of p̂ is approximately normal.

• No, because np = 50(0.59) = 29.5 ≥ 10 and n(1-p) = 50(0.41) = 20.5 ≥ 10, the sampling distribution of p̂ is not approximately normal.

• No, because np = 50(0.59) = 29.5 < 10 and n(1-p) = 50(0.41) = 20.5 < 10, the sampling distribution of p̂ is not approximately normal.

Suppose that 70% of all college women have been on a diet within the past 12 months. A sample survey interviews an SRS of 267 college women. Find the probability that 75% or more of the women in the sample have been on a diet.

(LT 6.4.3 #1)

• 0.0367

• 0.028

• 0.0371

• 0.371

Tags

CCSS.HSS.ID.A.4

Harley-Davidson motorcycles make up 14% of all the motorcycles registered in the United States. You plan to interview an SRS of 500 motorcycles owners.

Find the probability that 20% or more of the motorcycle owners in the sample own Harleys.

(LT 6.4.3 #2)

• 0.0155

• 0.14

• 0.0001

• 0.001

Tags

CCSS.HSS.ID.A.4