Question

Find the standardized length (z-score). Mean is 266 days and standard deviation is 16 days.

a. z-score for x= 290 days

Then find the probability that pregnancy occuured for the given lengths of times:

b. Prob. that pregnancy was between 250 days and 290 days

Answer 1

To find the standardized length (z-score), use the formula z = (x - mean) / standard deviation. For the given values, the z-score for x = 290 days is 1.5. To find the probability that pregnancy occurred between 250 days and 290 days, find the z-scores for those values and use a standard normal distribution table or calculator to find the probabilities. The probability is 0.5919.

Step-by-step explanation:

To find the standardized length (z-score), we can use the formula:

z = (x - mean) / standard deviation

a. For x = 290 days:

z = (290 - 266) / 16 = 1.5

b. To find the probability that pregnancy occurred between 250 days and 290 days, we need to find the area under the normal distribution curve between the z-scores for those values. We can use a standard normal distribution table or a calculator to find these probabilities. Let's first find the z-scores for 250 and 290:

z1 = (250 - 266) / 16 = -1

z2 = (290 - 266) / 16 = 1.5

Using the standard normal distribution table or a calculator, we can find the probabilities associated with these z-scores:

Prob(z < -1) = 0.1587

Prob(-1 < z < 1.5) = 0.4332

Adding these two probabilities gives us the probability that pregnancy occurred between 250 days and 290 days:

Prob(250 < x < 290) = 0.1587 + 0.4332 = 0.5919