Question

Find the area of the shaded region. The graph to the right depicts IQ scores of​ adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. The area of the shaded region is ??

106 122

2) The lengths of pregnancies are normally distributed with a mean of 267days and a standard deviation of 15 days. a. Find the probability of a pregnancy lasting 308 days or longer. b. If the length of pregnancy is in the lowest 22​%, then the baby is premature. Find the length that separates premature babies from those who are not premature

a. The probability that a pregnancy will last 308 days or longer is??? (Round to four decimal places as​ needed.)

b. Babies who are born on or before HOW MANY days are considered premature.(Round to the nearest integer as​ needed.)

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Answer 1

1)

Solution :

Given that ,

mean = $\mu$ = 100

standard deviation = $\sigma$ = 15

P(106 < x < 122) = P((106 - 100)/ 15) < (x - $\mu$ ) / $\sigma$ < (122 - 100) / 15) )

= P(0.4 < z < 1.47)

= P(z < 1.47) - P(z < 0.4)

= 0.9292 - 0.6554

= 0.2738

Area = 0.2738