Question

1) Adult Golden Retrievers have a mean weight of 64 pounds with a standard deviation of 8 pounds. If you take a random sample of 50 adult Golden Retrievers, what would be the standard deviation of the sample distribution, σ¯¯¯XσX¯?

• 64 pounds
• 1.13 pounds
• 8 pounds
• 9.05 pounds

2) Adult Golden Retrievers have a mean weight of 64 pounds with a standard deviation of 8 pounds. If you take a random sample of 35 gold retrievers, what is the probability the sample mean will be less than 65.5 pounds?

• 0.1335
• 0.8643
• 0.8665
• 0.1357

3) A random sample of 200 adults is taken from a population of 20000. It is believed that 86% of adults own a cell phone. Find the probability the sample proportion is between 84% and 87%

• The conditions for using the normal distribution have not been met
• .4530
• .4464
• 1.23

Answer 1

Solution:-

1) The standard deviation of the sample distribution is 1.1314.

2) The probability the sample mean will be less than 65.5 pounds is 0.134.

n = 35, Mean = 64, S.D = 8

x = 65.5

By applying normal distribution:-

z = 1.109

Use the z-score table or p-value calculator.

P(z > 1.109) = 0.134

3) The probability the sample proportion is between 84% and 87% is 0.4530.

p = 0.86, n = 200

p₁ = 0.84

p₂ = 0.87

By applying normal distribution:-

z₁ = - 0.815

z₂ = 0.4075

P( - 0.815 < z < 0.4075) = P(z > - 0.815) - P(z > 0.4075)

P( - 0.815 < z < 0.4075) = 0.7925 - 0.3418

P( - 0.815 < z < 0.4075) = 0.4507