HELP PLEASE ASAP 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?

0.8643

0.1357

0.8665

0.1335

Step-by-step explanation:

Let x be the random variable representing the mean weight of Adult Golden Retrievers. Assuming the weights are normally distributed(number of samples is greater than 30), we would apply the formula,

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = standard deviation

n = number of samples

From the information given,

µ = 64

σ = 8

n = 35

the probability that the sample mean will be less than 65.5 pounds is expressed as

P(x < 65.5)

For x = 65.5,

z = (65.5 - 64)/(8/√35) = 1.11

Looking at the normal distribution table, the probability corresponding to the z score is 0.8665

Therefore, the probability that the sample mean will be less than 65.5 pounds is 0.8665