Question

The mean incubation time for a type of fertilized egg kept at a certain temperature is 17 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day . Complete parts​ (a) through​ (e) below. ​

Part (a) Draw a normal model that describes egg incubation times of these fertilized eggs. ​

Part (b) Find and interpret the probability that a randomly selected fertilized egg hatches in less than days. The probability that a randomly selected fertilized egg hatches in less than 16 days is ____. ​(Round to four decimal places as​ needed.)

Interpret this probability. Select the correct choice below and fill in the answer box​(Round to the nearest integer as​ needed.)

A. If 100 fertilized eggs were randomly​ selected, exactly ____ would be expected to hatch on day 16 .

B. If 100 fertilized eggs were randomly​ selected, ____of them would be expected to hatch in less than 16 days.

C. In every group of 100 fertilized​ eggs, ____ eggs would be expected to hatch in less than 16 days.

Part ​(c) Find and interpret the probability that a randomly selected fertilized egg takes over 18 days to hatch. The probability that a randomly selected fertilized egg takes over days to hatch is ____. ​(Round to four decimal places as​ needed.)

Interpret this probability. Select the correct choice below and fill in the answer box ​(Round to the nearest integer as​ needed.)

A. If 100 fertilized eggs were randomly​ selected, exactly ____ would be expected to hatch on day 18.

B. If 100 fertilized eggs were randomly​ selected, ____ of them would be expected to take more than 18 days to hatch.

C. In every group of 100 fertilized​ eggs, ____ eggs would be expected to hatch in more than 18 days. ​

Part (d) Find and interpret the probability that a randomly selected fertilized egg hatches between and days. The probability that a randomly selected fertilized egg hatches between and days is nothing. ​(Round to four decimal places as​ needed.)

Interpret this probability. Select the correct choice below and fill in the answer box. ​(Round to the nearest integer as​ needed.)

A. If 100 fertilized eggs were randomly​ selected, ____ of them would be expected to hatch between 15 and 17 days.

B. In every group of 100 fertilized​ eggs, ____ eggs would be expected to hatch between 15 and 17 days.

C. If 100 fertilized eggs were randomly​ selected, exactly ____ would be expected to hatch on day 15 or on day 17. ​

Part (e) Would it be unusual for an egg to hatch in less than ​days? Why? The probability of an egg hatching in less than days is ____​, so it ____ (would or would not) be​ unusual, since the probability is ____ (less or greater) than 0.05. ​(Round to four decimal places as​ needed.)

Answer 1

a. The normal model of X is

time for a type X den otes the inenbation of forti lized egg X ~ N(M = 17, 6 = 0=1)

0.3 0.1 O 13 14 15 16 18 19 20 21 17 X

b) 17 < 16-17 P(x - Z ~ N(0.1) PlX < 16 Poz<-1) P(Z >) 1 - 0 (- 0.8.413 O. 1587 = If roo fertilized Bi eggs mere randomly therm selectedy Bolton 16 wroulld be expectad to hatch in less than days. 16 P(x P(X >18) - 17 >19-17) P(Z > 1) zanko,n) 11 0 (1) i D. 1587 eggs them If 100 fertilized selected, 16 of expected to take to hatch. were randomly would be than more 18 days

a) p(15 < x < X <17) P ( 15-17 -17 <17-17) 1 1 PC-2<zco Z ~ N(0,0) 00 Potz <2:) 0 (2) () 0.5 . 9772 - O.4772 J A. 100 fertilized eggs selected Nandomly 48 would be expected to between 15 of them hatch 17 days