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The lengths of a particular animal's pregnancies are approximately normally distributed, with mean \( \mu=266 \) days and standard deviation \( \sigma=16 \) days. (a) What proportion of pregnancies lasts more than 274 days? (b) What proportion of pregnancies lasts between 242 and 270 days? (c) What is the probability that a randomly selected pregnancy lasts no more than 238 days? (d) A "very preterm" baby is one whose gestation period is less than 230 days. Are very preterm babies unusual? (a) The proportion of pregnancies that last more than 274 days is 0.3085. (Round to four decimal places as needed.) (b) The proportion of pregnancies that last between 242 and 270 days is 0.5319 . (Round to four decimal places as needed.) (c) The probability that a randomly selected pregnancy lasts no more than 238 days is 0.0401 . (Round to four decimal places as needed.) (d) The probability of a "very preterm" baby is \( \square \). This event \( \square \) unusual because the probability is \( \square \) than 0.05 .

The lengths of a particular animal's pregnancies are approximately normally distributed, with mean \( \mu=266 \) days and standard deviation \( \sigma=16 \) days. (a) What proportion of pregnancies lasts more than 274 days? (b) What proportion of pregnancies lasts between 242 and 270 days? (c) What is the probability that a randomly selected pregnancy lasts no more than 238 days? (d) A "very preterm" baby is one whose gestation period is less than 230 days. Are very preterm babies unusual? (a) The proportion of pregnancies that last more than 274 days is (Round to four decimal places as needed.)

The number of chocolate chips in an 18 -ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chip (a) What is the probability that a randomly selected bag contains between 1100 and 1400 chocolate chips, inclusive? (b) What is the probability that a randomly selected bag contains fewer than 1125 chocolate chips? (c) What proportion of bags contains more than 1200 chocolate chips? (d) What is the percentile rank of a bag that contains 1050 chocolate chips? (a) The probability that a randomly selected bag contains between 1100 and 1400 chocolate chips, inclusive, is (Round to four decimal places as needed.)

Assume the random variable \( X \) is normally distributed with mean \( \mu=50 \) and standard deviation \( \sigma=7 \). Find the 97 th percentile. The 97 th percentile is (Round to two decimal places as needed.)

Assume the random variable \( X \) is normally distributed with mean \( \mu=50 \) and standard deviation \( \sigma=7 \). Find the 77 th percentile. The 77 th percentile is 55.39 . (Round to two decimal places as needed.)

Assume the random variable \( X \) is normally distributed with mean \( \mu=50 \) and standard deviation \( \sigma=7 \). Find the 77 th percentile. The 77 th percentile is (Round to two decimal places as needed.)

What percent of the population has an intelligence quotient below 100?A. 75% B. 50% C. 35% D. 10%

Assume the random variable X is normally distributed, with mean \( \mu=48 \) and standard deviation \( \sigma=8 \). Find the 12 th percentle The 12 th percentile is (Round to two decimal places as needed.)

Question 21 SEAGULLS A biologist studying seagulls estimates that \( 5 \% \) of the seagulls in a flock have been banded. If 22 of the seagulls have been banded, approximately how many seagulls are in the flock? \( \begin{array}{ll}\text { A) } 110 \\ \text { B) } 440 \\ \text { C) } 1100 \\ \text { D) } 4400\end{array} \)

Find the value of \( z_{a} \) The value of \( z_{0.32} \) is \( \square \). (Round to two decimal places as needed.)