Question

HEP BEING TIMED!

Answer 1

Answer:

Step-by-step explanation:

Let x be the random variable representing the length of pregnancies in giraffes. Since it is normally distributed and the population mean and population standard deviation are known, 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 = 430

σ = 9

n = 25

the probability that the sample mean length will be between 429 days and 432 days is expressed as

P(429 ≤ x ≤ 432)

For x = 429,

z = (429 - 430)/(9/√25) = - 0.56

Looking at the normal distribution table, the probability corresponding to the z score is 0.288

For x = 432,

z = (432 - 430)/(9/√25) = 1.11

Looking at the normal distribution table, the probability corresponding to the z score is 0.867

Therefore,

P(429 ≤ x ≤ 432) = 0.867 - 0.288 = 0.579