Question

Approximately 10% of all people are left-handed. Consider a grouping of fifteen people. (5.3.4)

a) State the random variable.

b) Write the probability distribution.

c) Draw a histogram.

d) Describe the shape of the histogram.

e) Find the mean.

f) Find the variance.

g) Find the standard deviation.

Answer 1

Solution:

Answer: By using given information, (a) weet x denote the number of left handed people. (b) the number of trials fixed n = 15 paobability of success is p=0.10 the paro bability distribution function is, P(x= x)- () pt (1-P)n-* .10)(1-0.10)'5-4. (c) using MEGASTAT, the histogram is Shacon below: Binomial distəribution (n =P-0.1) 2 0.40 0:35 o Series 1 0.30 D.257 0.20 0.15 0.05 Doch 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

do the shape of the histogram is skeweed to dlight- (e) The pagameleos porovided for the . Binomial Distribution are n= 15, P=0.10 the population mean is computed as: M = n. P - 15 *010 Il = 1.5] (f) the population variance as obtained asing the following foormula : .. 02= np (1-P) = 15*0.10 (-0.1) = 15 *0.10 *0.9 Tor: 1.35) (19) The Standard deviation is com Deated by taking the squared root of the Vcoüance : o. Th.pci-p) - 11.35 To=1.1619