Question

A recent study has shown that 28% of 18-34 year olds check their Facebook/Instagram feeds before getting out of bed in the morning,

If we sampled a group of 150 18-34 year olds, what is the probability that the number of them who checked their social media before getting out of bed is:

a.) At least 34?

b.) No more than 50?

c.) between 40 and 44 (including 40 and 44)?

Use the Normal Approximation to the Binomial distribution to answer this question.

Student scores on Professor Combs' Stats final exam are normally distributed with a mean of 75 and a standard deviation of 6.8

Find the probability of the following:

**(use 4 decimal places)**

a.) The probability that one student chosen at random scores above an 80.

b.) The probability that 20 students chosen at random have a mean score above an 80.

c.) The probability that one student chosen at random scores between a 70 and an 80.

d.) The probability that 20 students chosen at random have a mean score between a 70 and an 80.

Answer 1

A recent study Given = t-28 00 72 h-150 meam = np 150X.28 Hardaid deviaton pq 42 E30-24 NisOXa2802 5-4991 let X denote no-ol c34 yeasolds coho checkad then sacial media belose qetting out of bed a) atleast 34 PX>34 on stardasdiging PIZ34-42 1 5.4991 PZZS 5499 - PZ--4543 1 we requive the avea o shaded xegion PIZ-4550-5+ P1-4554740 0-5+ 0.4272 0.9212 -1455

Probability that atleast 34 0 them oho hecked their gocial media. belore bed is gelting out O.9292 b No more than 50 PX 250 standardiging PX-H Z50-H -PIZL50-42 54991 PIZZS 5.499 we reaure the area egion P[Z Z1-4550St Pl0zC1455 shaded 1.나55 0.5+0-4272 =0-9272 The probability that no more than 50 who checked their souial media belore getting out bed ts them O.9212

) between 40 and 44 P40X44 tandardiging PI40-42トX-42244-42 ら4901 5.4991 ら4991 P - 2 5-4991 5 499 P-0.3631 4ZED3631 PIZI0-2631P2103 0-36 2 X P0L7L0.36-0-3631 - 2X0. 1400 0.2812 The p2obability that numbes o them oho checked theix sodial media before gefhng out ol bed ts between 40 ard 44 ts 0 2812

Student goses on Given, 6.8 -denote student's score on tinal exam a) To Jind the pohabiliby that one student choien at andom SLOres above an s6. PX So Standendging PX-H20-H PZS0-75 6.8 P2PZ0-135] PIZ5 6.8 we require the area ol shaded region PZ0735 0-S-P0L20795 0.5-0.26885 -0.2315 O7.35 =0.2312 The probabilty that one student chosen at above anso fs 0 2312 andom sloreo

b)"o nd the paobabilty that 20 students chosen at sandom have a mean ScOre above sO 20 student's X denote mean o PXSO Here 80 standarding P Score 80-15 6. A20 - PZ25XS20 PZ8a.36 6.8 3-29 1 chaded the ara we eauire e gon 22יר =0-5-Pl0Z2329 =0.5-0.4995 3.29 = 0.0005 20 students chosen at The paobabiltty that andom have amean score above go s 0.0005

c) To ind the pohaloilty that one student chosen at andom scoreo between a 10 and an 86 andandging 104ZX- s0uP10-5 Z80-15 68 P-5 LZ5 0.74 Z4074 P 6 8 P IZI074 we sequre aea agion PIZI2014 2XP0L210404 haded : 2X 0. 2104 -0.5403 The probability that chosen at one stud ent between a sandom Scoreo s O.5408 0 and an 80

d) The pchabiltby that 20 rtudents chosen d Yandom have 70 and an 80 a mean. Score between a 20 students mean scOYe chosen at adl om dandardtng P0-LL X- 80- P0-75 2Z 80-75 68 A20 P-329743-29 -5 225 1.52 152 PIZI23292X P Plozzz329 the we require area shaded 2agton 3-R9 2XP 02Z3 aa2x 0.4995 0-999 The paohability that 20 Student chosen at andom have a mean 40 and SLOxe between a go is 0.9996 an
A recent study...,

a)At least 34

The probability that number of them who checked their social media before getting out of bed is at least 34 is 0.9272.

b) No more than 50

The probability that the number of them who checked their social media before getting out of bed is no more than 50 is 0.9272.

c) between 40 and 44

The probability that the number of them who checked their social media before getting out of bed is between 40 and 44 is 0.2812.

Students scores on......,

a.) The probability that one student chosen at random scores above an 80 is 0.2312.

b.) The probability that 20 students chosen at random have a mean score above 80 is 0.0005.

c.) The probability that one student chosen at random scores between a 70 and an 80 is 0.5408.

d.) The probability that 20 students chosen at random have a mean score between a 70 and an 80 is 0.9990.